Related papers: Pseudoclassical description of scalar particle in …
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
We construct a locally supersymmetric action for the scalar particle, and study its relation with the usual reparametrization invariant action. The mechanisms at work are similar to those employed in the embedding of the bosonic string into…
We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations…
At the classical level, the SU(2/1) superalgebra offers a natural description of the elementary particles: leptons and quarks massless states, graded by their chirality, fit the smallest irreducible representations of SU(2/1). Our new…
The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure…
I propose a discrete model for the Gell-Mann matrices, which allows them to participate in discrete symmetries of three generations of four types of elementary fermions, in addition to their usual role in describing a continuous group…
We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free…
We give an action for the massless spinning particle in pseudoclassical mechanics by using grassmann variables. The constructed action is invariant under $\tau $-reparametrizations, local SUSY and O(N) transformations. After quantization,…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the saddle…
A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the…
We present a (1+1)-dimensional fermionic QFT with non-local couplings between currents. This model describes an ensemble of spinless fermions interacting through forward, backward and umklapp scattering processes. We express the vacuum to…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally.…