Journal of Mathematical Physics, since 1960, publishes some of the best papers from outstanding mathematicians and physicists. It was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods suitable for such applications and for the formulation of physical theories.
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Multitime wave functions are wave functions that have a time variable for every particle, such as . They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for noninteracting particles, it is a challenge to set up consistent multitime equations with interaction. We prove for a wide class of multitime Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multitime wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cutoff length δ > 0 is introduced (in the sense that the multitime wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multitime Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cutoff, the resulting multitime equations are interactionfree, which supports the conclusion expressed in the title.

We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding socalled “sequence of secondary measures problem” and give them a physical interpretation.

We study the propagation of ultrashort short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multiscale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

In our previous paper, we classified linearly compact algebraic simple N = 6 3algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3dimensional ChernSimons theories.

We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and with an arbitrary coherent laser field. We assume that the oscillator is initially in thermodynamic equilibrium with its environment, a nonfactorized initial density matrix of the system and the environment, and that at t = 0 the modulation of the frequency, the coupling to the incoherent and the coherent radiation are switched on. The subsequent dynamics, induced by the presence of the blackbody radiation, the laser field, and the frequency modulation, is studied in the framework of the influence functional approach. This approach allows incorporating, in analytic closed formulae, the nonMarkovian character of the oscillatorenvironment interaction at any temperature as well the nonMarkovian character of the blackbody radiation and its zeropoint fluctuations. Expressions for the time evolution of the covariance matrix elements of the quantum fluctuations and the reduced densityoperator are obtained.