Related papers: Note on the super-extended Moyal formalism and its…
The BV formalism is a well-established method for analyzing symmetries and quantization of field theories. In this paper we use the BV formalism to derive partition functions of gauge invariant operators up to equations of motions and their…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view to deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the BRS invariance and it is…
We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both…
We present a superfield formulation of the quantization program for theories with first class constraints. An exact operator formulation is given, and we show how to set up a phase-space path integral entirely in terms of superfields. BRST…
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which in particular ascribes trajectories to…
We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when…
The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the…
We adopt the Y-formalism to study beta-gamma systems on hypersurfaces. We compute the operator product expansions of gauge-invariant currents and we discuss some applications of the Y-formalism to model on Calabi-Yau spaces.
A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space…
The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space…
Path integral techniques in collective fields are shown to be a useful analytical tool to reformulate a field theory defined in terms of microscopic quark (gluon) degrees of freedom as an effective theory of collective boson (meson) fields.…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
In this work the possibility of detecting the presence of a Yukawa term, as an additional contribution to the usual Newtonian gravitational potential, is introduced. The central idea is to analyze the effects at quantum level employing…
Hamilton's action principle is formulated and extended in conformity with the gauge transformations underlying Weyl's geometry. The extended principle characterizes infinitely many equally likely trajectories with a particle traveling along…
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…
We define the notion of distribution on an infinite dimensional space motivated by the notion of Feynman path integral and by construction of probability measures for generalized random fields. This notion of distribution turns out to be…