International Journal of Modern Physics A

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides — coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.

We give an explicit quantum super field construction of the super-Casimir algebras, which is obtained from supersymmetric Miura transformation for the Lie super-algebra . And also we give an extension of this algebras including a super-vertex operator which depends on simple root system of .

This work shows that the quantum calculation of the energy exchanged between gravitational waves and resonating antennas contains a term linear in the Riemann tensor if the oscillator is supposed to be in a coherent state, while it contains only quadratic terms if it is in a stationary state. In some cases the latter hypothesis, presently accepted in the literature, underestimates the sensitivity of GW antennas by several orders of magnitude. The authors show the need for the correction of the error, while its origin and consequences are explained.

Plausible interrelations between parameters of the standard model are studied. The empirical value of the top quark mass, when used in the renormalization group equations, suggests that the ratio of the color SU(3) gauge coupling g₃, and the top coupling g_t is independent of the renormalization scale. On the other hand, the variety of top-condensate models suggests that the Higgs self-coupling λ is proportional to . Invoking the requirement that the ratio is independent of the renormalization scale t, fixes the Higgs mass. The pole mass of the Higgs (which differs from the renormalization group mass by a few percent) is found to be ~ 154 GeV for the one-loop equations and ~ 148 GeV for the two-loop equations.

The classical motion of spinning particles can be described without recourse to particular models or special formalisms, and without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincaré group; and only requiring the conservation of the linear and angular momenta, we derive the zitterbewegung, namely the decomposition of the four-velocity in the usual Newtonian constant term p^μ/m and in a non-Newtonian time-oscillating spacelike term. Consequently, free classical particles do not obey, in general, the Principle of Inertia. Superluminal motions are also allowed, without violating special relativity, provided that the energy–momentum moves along the worldline of the center-of-mass. Moreover, a nonlinear, nonconstant relation holds between the time durations measured in different reference frames. Newtonian mechanics is reobtained as a particular case of the present theory: namely for spinless systems with no zitterbewegung. Then we analyze the strict analogy between the classical zitterbewegung equation and the quantum Gordon-decomposition of the Dirac current. It is possible a variational formulation of the theory, through a Lagrangian containing also derivatives of the four-velocity: we get an equation of the motion, actually a generalization of the Newton law a=F/m, where non-Newtonian zitterbewegung-terms appear. Requiring the rotational symmetry and the reparametrization invariance we derive the classical spin vector and the conserved scalar Hamiltonian, respectively. We derive also the classical Dirac spin (a×v)/4m and analyze the general solution of the Eulero–Lagrange equation oscillating with the Compton frequency ω=2m. The interesting case of spinning systems with zero intrinsic angular momentum is also studied.

We consider the existence of a Noether symmetry in the scalar–tensor theory of gravity in flat Friedman–Robertson–Walker (FRW) cosmology. The forms of coupling function ω(ϕ) and generic potential V(ϕ) are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.

We use holomorphic factorization to find the partition functions of an Abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that previously has been found in a Hamiltonian formulation.

For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order to illustrate our proof we work out explicitly the cases of a fractional spin particle in 2+1 dimensions and the original Brink–Schwarz massless superparticle in D=10 dimensions in a Lorentz-covariant constraints separation.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV–BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV–BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

We study a scale-invariant two measures theory where a dilaton field ϕ has no explicit potentials. The scale transformations include the translation of a dilaton ϕ→ϕ+ const. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for ϕ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state p_ϕ=wρ_ϕ where w is predicted to be restricted by -1<w<-0.82. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, the energy–momentum tensor is canonical and the "fifth force" is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.