On the Gauge Invariance of the Transition Probability of a Charged Particle in Electromagnetic Field

This paper suggests a principle to find a unitary operator U which transforms non-physical quantity,zero-potential Hamiltonian Ho, into true physical quantity UHoU for a charged particle in classical electromagneticfield, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Differentmethods correspond to different unitary operators which satisfy the above-mentioned principle.     

Hidden global conformal symmetry without Virasoro extension in theory of elasticity

The theory of elasticity (a.k.a. Riva–Cardy model) has been regarded as an example of scale invariant but not conformal field theories. We argue that in d=2$d=2$ dimensions, the theory has hidden global conformal symmetry of SL(2,R)×SL(2,R)$SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ without its Virasoro extension. More precisely, we can embed all the correlation functions of the displacement vector into a global conformal field theory with four-derivative action in terms of two scalar potential variables, which necessarily violates the reflection positivity. The energy–momentum tensor for the potential variables cannot be improved to become traceless so that it does not show the Virasoro symmetry even with the existence of global special conformal current.     

Asymptotic Self-similarity Breaking in Cosmology

We discuss the role of self-similarity in the evolution of cosmological models. The simplest model, the flat Friedmann–Lematre universe is exactly self-similar. On the other hand, the open Friedmann–Lematre universe and the anisotropic Bianchi I universes, are not exactly self-similar, but are asymptotically self-similar, both near the initial singularity and at late times. In general, however, cosmological models are not asymptotically self-similar, and our goal is to describe the different mechanisms that lead to asymptotic self-similarity breaking in Bianchi universes. The discussion will also serve to give an overview of our current understanding of the dynamics of Bianchi universes.     

Local Poincaré Symmetry in Gauge Theory of Gravity

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.     

Gauge invariance in braneworld scenarios

Rubakov and Shaposhnikov (RSH), in a seminal paper, discussed the possibility that particles are confined in a potential well. This is considered as the first mention to the today?s idea that we live in a brane, i.e., the braneworld concept. In this work we show precisely that the proposed RSH model has a gauge invariant equivalent action and we discuss it in the light of braneworld structure. We analyzed the intrinsic features of both models trying to disclose new properties within RSH braneworld theory.     

关于Noether对称性的两种理解

介绍了对Lagrange系统Noether对称性的两种理解，一种理解为Lagrange函数的不变性，另一种理解为作用量的不变性.研究表明，这两种理解是不同的.在一些条件下，Lagrange函数的不变性可以成为作用量的不变性，在另一些条件下，作用量的不变性可以成为Lagrange函数的不变性.将Noether对称性理解为作用量的不变性是合理的. 关键词： Lagrange系统 Noether对称性 作用量的不变性 Lagrange函数的不变性     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

Conservative Currents of Boundary Charges in AdS2 1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2- 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.``     

Radiative effects and dimension 5 operators arising from quantum gravity

We examine radiative corrections arising from Lorentz violating dimension five operators presumably associated with Planck scale physics as recently considered by Myers and Pospelov. We find that observational data result in bounds on the dimensionless parameters of the order 10^–15. These represent the most stringent bounds on Lorentz violation to date.     

Infinitely many shape invariant potentials and new orthogonal polynomials

Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic Pöschl–Teller potentials in terms of their degree ℓ polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (ℓ=1,2,…) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and Gómez-Ullate et al.'s are the first members of these infinitely many potentials.     

Symmetries and the compatibility condition for the new translational shape invariant potentials

In this Letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape invariance condition. We focus on the recent examples of Odake and Sasaki (infinitely many polynomial, continuous l and multi-index rational extensions). As a byproduct, we obtain new relations, to the best of our knowledge, for Laguerre, Jacobi polynomials and (confluent) hypergeometric functions.     

间隔不变性与相对论拉格朗日力学

文章证明由时空和速度间隔不变性可以导出相对论哈密顿和拉格朗日力学，由此说明哈密顿或拉格朗日为洛仑兹不变量是时空和速度间隔不变性的必然结果。     

双环形振子的超对称性

研究了双环形振子(DRSO)的超对称性和形不变性,并得到了DRSO的能量本征值和能量本征函数     

Proof of perturbative gauge invariance for tree diagrams to all orders

It is proved that classical BRS‐invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Lagrangian of gravity.     

A manifestly gauge-invariant description of interaction of atomic systems with strong fields in the dipole approximation

We propose a new type of gauge-invariant expansion of the ionization probability amplitudes of atoms by short pulses of electromagnetic radiation. Contrary to previous gauge-invariant approaches to this problem it does not require different partitions of the total Hamiltonian depending on the choice of gauge. In a natural way the atomic potential is treated as perturbation acting on an electron interacting with strong pulse. Whereas this is a standard assumption of strong field approximation (SFA), we show that grouping consequently together all terms of the same order in the atomic potential results in the expansion of the amplitude which is gauge invariant order by order, and not only in the limit of infinite series. In this approach, which is illustrated by numerical examples, the “direct ionization” and “rescattering” contributions are different from those commonly used in SFA-calculations.     

Conservative Currents of Boundary Charges in AdS2+1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2+1)-dimensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.     

Letter: Ultra-High Energy Cosmic Rays and Symmetries of Spacetime

High energy cosmic rays allow probing phenomena that are inaccessible to accelerators. Observation of cosmic rays, presumably protons, with energies beyond 4 × 10¹⁹ eV, the so-called Greisen-Zatsepin-Kuzmin (GZK) cut-off, give origin to two puzzles: How do particles accelerate to such energies ? Are their sources within 50–100 Mpc from Earth, or Lorentz invariance is actually a broken symmetry ? We suggest an astrophysical test to verify the latter alternative and explore a possible connection with an alternative theory of gravity that exhibits preferred-frame effects.     

Schrödinger invariance and strongly anisotropic critical systems

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent =z=2, the group of local scale transformation considered is the Schrödinger group, which can be obtained as the nonrelativistic limit of the conformal group. The requirement of Schrödinger invariance determines the two-point function in the bulk and reduces the three-point function to a scaling form of a single variable. Scaling forms are also derived for the two-point function close to a free surface which can be either spacelike or timelike. These results are reproduced in several exactly solvable statistical systems, namely the kinetic Ising model with Glauber dynamics, lattice diffusion, Lifshitz points in the spherical model, and critical dynamics of the spherical model with a nonconserved order parameter. For generic values of , evidence from higher-order Lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two-point function.     

What price the spin-statistics theorem?

We examine a number of recent proofs of the spin-statistics theorem. All, of course, get the target result of Bose-Einstein statistics for identical integral spin particles and Fermi-Dirac statistics for identical half-integral spin particles. It is pointed out that these proofs, distinguished by their purported simple and intuitive kinematic character, require assumptions that are outside the realm of standard quantum mechanics. We construct a counterexample to these non-dynamical kinematic ‘proofs’ to emphasize the necessity of a dynamical proof as distinct from a kinematic proof. Sudarshan’s simple non-relativistic dynamical proof is briefly described. Finally, we make clear the price paid for any kinematic ‘proof’.     

Separability,gauge invariance and nonsuperluminality in direct interaction dynamics

We discuss the classical mechanics of relativistic systems with direct interaction. We show that various desiderata can all be accommodated in the single time approach by restricting the observables to the gauge invariant variables. We show how such observables can be constructed in general. We explicitly construct position observables in a general system and show that they lead to separable, invariant world lines. Nonsuperluminality is explicitly demonstrated for two body systems interacting via central forces of semibounded magnitude provided they ensure timelike canonical momenta. For two particles, our results reproduce the usual solution in covariant equal-time gauge.