Semiclassical probability of radiation of twisted photons in the ultrarelativistic limit

Abstract We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.

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Is Relativistic Quantum Mechanics Compatible with Special Relativity?

Zeitschrift für Naturforschung A ◽

10.1515/zna-2001-0503 ◽

2001 ◽

Vol 56 (5) ◽

pp. 347-365

Author(s):

B. H. Lavenda

Keyword(s):

Quantum Mechanics ◽

Wave Equation ◽

Finite Difference ◽

Special Relativity ◽

Bessel Function ◽

Nonrelativistic Limit ◽

Phase Factor ◽

Wave Number ◽

Modified Bessel Function ◽

Ultrarelativistic Limit

Abstract The transformation from a time-dependent random walk to quantum mechanics converts a modified Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schrödinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an integrating factor is required which determines how the intensity decays in time. The phase correlation between neighboring sites in quantum mechanics is given by the phase factor for the electron to reverse its direction, whereas, in special relativity, it is given by the Doppler shift.

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Ultrarelativistic Spinning Particle and a Rotating Body in External Fields

Advances in High Energy Physics ◽

10.1155/2016/1376016 ◽

2016 ◽

Vol 2016 ◽

pp. 1-27 ◽

Cited By ~ 22

Author(s):

Alexei A. Deriglazov ◽

Walberto Guzmán Ramírez

Keyword(s):

Electromagnetic Field ◽

Three Dimensional ◽

Vector Model ◽

Maximum Speed ◽

Field Interaction ◽

Spinning Particle ◽

Spin Field ◽

Field Coupling ◽

Rotating Body ◽

Ultrarelativistic Limit

We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle’s trajectory in ultrarelativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultrarelativistic limit. In particular, three-dimensional acceleration of the particle becomes infinite in the limit. Therefore, we examine the nonminimal interaction through the gravimagnetic momentκand show that the theory withκ=1is free of the problems detected in MPTD equations. Hence, the nonminimally interacting theory seems a more promising candidate for description of a relativistic rotating body in general relativity. Vector model in an arbitrary electromagnetic field leads to generalized Frenkel and BMT equations. If we use the usual special-relativity notions for time and distance, the maximum speed of the particle with anomalous magnetic moment in an electromagnetic field is different from the speed of light. This can be corrected assuming that the three-dimensional geometry should be defined with respect to an effective metric induced by spin-field interaction.

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BMS modules in three dimensions

International Journal of Modern Physics A ◽

10.1142/s0217751x16500688 ◽

2016 ◽

Vol 31 (12) ◽

pp. 1650068 ◽

Cited By ~ 39

Author(s):

A. Campoleoni ◽

H. A. Gonzalez ◽

B. Oblak ◽

M. Riegler

Keyword(s):

Three Dimensions ◽

Unitary Representations ◽

Induced Representations ◽

Highest Weight ◽

Higher Spin ◽

Ultrarelativistic Limit ◽

Highest Weight Representations

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and [Formula: see text] algebras, which is to be contrasted with nonrelativistic limits that typically give nonunitary representations. To support this dichotomy, we also point out that the ultrarelativistic and nonrelativistic limits of generic [Formula: see text] algebras differ in the structure of their nonlinear terms.

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Screening masses of photons interacting with a two-species fermionic system in relativistic BCS–BEC crossover

International Journal of Modern Physics B ◽

10.1142/s0217979217500783 ◽

2017 ◽

Vol 31 (11) ◽

pp. 1750078

Author(s):

Xun Huang ◽

Wei-Min Cai ◽

Hao Guo

Keyword(s):

Mechanical Stability ◽

Nonrelativistic Limit ◽

Superfluid Density ◽

Einstein Condensation ◽

Number Density ◽

Fermionic System ◽

Self Energy ◽

Ultrarelativistic Limit ◽

Bose Einstein ◽

Electromagnetic Instability

We address the behavior of Debye and Meissner masses of photons in a condensate of fermion pairs in the presence of number density asymmetry. Our formalism applies to a two-species fermionic system with number density asymmetry in BCS–Bose–Einstein condensation (BEC)–relativistic BEC crossover and with variable rapidity. Our results recover the known results of the photon self-energy in the ultrarelativistic limit and the superfluid density in the nonrelativistic limit. We further consider the electromagnetic stability of the condensate and show that the Meissner mass squared can become negative in the weakly coupling BCS regime and the strongly coupling relativistic BEC regime. The electromagnetic instability is compared to the mechanical stability discussed in previous works.

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