We study the radiation reaction in Lorentz-violating electrodynamics [D. Colladay and V. Alan Kos... more We study the radiation reaction in Lorentz-violating electrodynamics [D. Colladay and V. Alan Kostelecky, Phys. Rev. D 58, 116002 (1998)]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However, it turns out that radiation reaction receives no change due to Lorentz violation, whereas electromagnetic mass manifests anisotropy.
Classical physics encompasses the study of physical phenomena which ranges from local (a point) t... more Classical physics encompasses the study of physical phenomena which ranges from local (a point) to nonlocal (a region) in space and/or time. We discuss the concept of spatial and temporal nonlocality. However, one of the likely implications pertaining to nonlocality is non-causality. We study causality in the context of phenomena involving nonlocality. An appropriate domain of space and time which preserves causality is identified.
We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the ret... more We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the retarded fields. The derivation is simple and at the same time pedagogically accessible. We obtain the radiation reaction for a charged particle moving in a conic. We pin down the underlying concept of mass renormalization.
We study the radiation reaction acting on an accelerating charge moving in noncommutative spaceti... more We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the pre-acceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimen... more In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don't comply with the standard inner and outer horizon classification for de...
We study a system of a finite size charged particle interacting with radiation field by exploitin... more We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for graduate courses on advanced electrodynamics and classical theory of fields.
We generalize the derivation of electromagnetic fields of a charged particle moving with a consta... more We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic transformations of electromagnetic fields and Thomson's construction [2]. We derive the average Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded time.
We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moy... more We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moyal spacetime using twisted commutation relations. We obtain the relevant twisted bosonization rules. We show that there exists dual rela- tionship between twisted bosonic and fermionic operators. The strong-weak duality is also observed to be preserved as its commutative counterpart.
We consider the possibility that there may be causality violation detectable at higher energies. ... more We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar nonlocal theory containing a mass scale Λ as a model example and make a preliminary study of how the causality violation can be observed. We show how to formulate an observable whose detection would signal causality violation. We study the range of energies (relative to Λ) and couplings to which the observable can be used.
We study causality in non-commutative quantum field theory with a space-space non-commutativity. ... more We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian ψ(x) ⋆ ψ(x) ⋆ φ(x), is observed to be causality violating even in case of space-space noncommutativity for which θ 0i = 0. 1
We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as sugges... more We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as suggested by the study of causality in presence of bound states in this model). We study the bound state formation in the model. In the limit $g\to\infty,M\to\infty$, in a certain specific manner, we show that there are a large number of bound states of which at least the low lying states are described by the non-relativistic Schrodinger equation. We show that, in this limit, the excited bound states are unstable and deem to decay quickly (lifetime $\tau\to 0 $) by emission of scalar (s) in this particular limit. The mass of the ground state is not significantly affected by higher order quantum corrections and by proper choice of parameters, involving only small changes, can be adjusted to be equal to the mass of the scalar. As a result of quantum effects, the state of the meson mixes with the lowest bound state and may be dominated by the latter .We show that in this detailed sense, a scalar ...
We study causality in non-commutative quantum field theory with a space-space non-commutativity. ... more We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian ψ(x) ⋆ ψ(x) ⋆ φ(x), is observed to be causality violating even in case of space-space noncommutativity for which θ = 0.
We study the radiation reaction acting on an accelerating charge moving in noncommutative spaceti... more We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the preacceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
In this paper, we analyze the causal aspects of evolving marginally trapped surfaces in a Ddimens... more In this paper, we analyze the causal aspects of evolving marginally trapped surfaces in a Ddimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don’t comply with the standard inner and outer horizon classification for degener...
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible m... more We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
International Journal of Geometric Methods in Modern Physics
We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them i... more We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them in terms of their local plane wave behavior. We estimate the local spectrum of wave numbers by approximating the Spherical harmonics in the locally flat neighborhood around a point on the Spheres. These local wave numbers are shown to obey an interesting Pythagorean type relation. Based on this relation, we propose a question whether there are integer triples for 2-spheres and their generalization to n-spheres. We apply the local spectrum to define quantities such as phase velocity and group velocity on a sphere and outline the relevance of the analysis for the case fields on de Sitter space.
We study the radiation reaction in Lorentz-violating electrodynamics [D. Colladay and V. Alan Kos... more We study the radiation reaction in Lorentz-violating electrodynamics [D. Colladay and V. Alan Kostelecky, Phys. Rev. D 58, 116002 (1998)]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However, it turns out that radiation reaction receives no change due to Lorentz violation, whereas electromagnetic mass manifests anisotropy.
Classical physics encompasses the study of physical phenomena which ranges from local (a point) t... more Classical physics encompasses the study of physical phenomena which ranges from local (a point) to nonlocal (a region) in space and/or time. We discuss the concept of spatial and temporal nonlocality. However, one of the likely implications pertaining to nonlocality is non-causality. We study causality in the context of phenomena involving nonlocality. An appropriate domain of space and time which preserves causality is identified.
We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the ret... more We derive the Lorentz self force for an arbitrarily moving charged particle via averaging the retarded fields. The derivation is simple and at the same time pedagogically accessible. We obtain the radiation reaction for a charged particle moving in a conic. We pin down the underlying concept of mass renormalization.
We study the radiation reaction acting on an accelerating charge moving in noncommutative spaceti... more We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the pre-acceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimen... more In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don't comply with the standard inner and outer horizon classification for de...
We study a system of a finite size charged particle interacting with radiation field by exploitin... more We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for graduate courses on advanced electrodynamics and classical theory of fields.
We generalize the derivation of electromagnetic fields of a charged particle moving with a consta... more We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic transformations of electromagnetic fields and Thomson's construction [2]. We derive the average Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded time.
We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moy... more We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moyal spacetime using twisted commutation relations. We obtain the relevant twisted bosonization rules. We show that there exists dual rela- tionship between twisted bosonic and fermionic operators. The strong-weak duality is also observed to be preserved as its commutative counterpart.
We consider the possibility that there may be causality violation detectable at higher energies. ... more We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar nonlocal theory containing a mass scale Λ as a model example and make a preliminary study of how the causality violation can be observed. We show how to formulate an observable whose detection would signal causality violation. We study the range of energies (relative to Λ) and couplings to which the observable can be used.
We study causality in non-commutative quantum field theory with a space-space non-commutativity. ... more We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian ψ(x) ⋆ ψ(x) ⋆ φ(x), is observed to be causality violating even in case of space-space noncommutativity for which θ 0i = 0. 1
We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as sugges... more We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as suggested by the study of causality in presence of bound states in this model). We study the bound state formation in the model. In the limit $g\to\infty,M\to\infty$, in a certain specific manner, we show that there are a large number of bound states of which at least the low lying states are described by the non-relativistic Schrodinger equation. We show that, in this limit, the excited bound states are unstable and deem to decay quickly (lifetime $\tau\to 0 $) by emission of scalar (s) in this particular limit. The mass of the ground state is not significantly affected by higher order quantum corrections and by proper choice of parameters, involving only small changes, can be adjusted to be equal to the mass of the scalar. As a result of quantum effects, the state of the meson mixes with the lowest bound state and may be dominated by the latter .We show that in this detailed sense, a scalar ...
We study causality in non-commutative quantum field theory with a space-space non-commutativity. ... more We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian ψ(x) ⋆ ψ(x) ⋆ φ(x), is observed to be causality violating even in case of space-space noncommutativity for which θ = 0.
We study the radiation reaction acting on an accelerating charge moving in noncommutative spaceti... more We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the preacceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
In this paper, we analyze the causal aspects of evolving marginally trapped surfaces in a Ddimens... more In this paper, we analyze the causal aspects of evolving marginally trapped surfaces in a Ddimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don’t comply with the standard inner and outer horizon classification for degener...
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible m... more We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
International Journal of Geometric Methods in Modern Physics
We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them i... more We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them in terms of their local plane wave behavior. We estimate the local spectrum of wave numbers by approximating the Spherical harmonics in the locally flat neighborhood around a point on the Spheres. These local wave numbers are shown to obey an interesting Pythagorean type relation. Based on this relation, we propose a question whether there are integer triples for 2-spheres and their generalization to n-spheres. We apply the local spectrum to define quantities such as phase velocity and group velocity on a sphere and outline the relevance of the analysis for the case fields on de Sitter space.
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Papers by Asrarul Haque