Related papers: A new path integral representation for the thermal…
In this paper we present a method with which it is possible to describe a dissipative system in Lagrangian formalism, without the trouble of finding the proper way to model the environment. The concept of the presented method is to create a…
Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by the incorporation of the self-adjoint extension method to the path integral formalism. The energy-dependent Green functions for free particle plus…
We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a…
The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms…
We present a theoretical framework on non-local classical field theory using fractional integrodifferential operators. Due to the lack of easily manageable symmetries in traditional fractional calculus and the difficulties that arise in the…
A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
In Hamiltonian mechanics the equations of motion may be considered as a condition on the tangent vectors to the solution; they should be null-vectors of the symplictic structure. Usually the formalism for the field case is done by replacing…
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the…
The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
We derive a simple calculation rule for Aoyama--Tamra's prescription for path integral with degenerated potential minima. Non-perturbative corrections due to the restricted functional space (fundamental region) can systematically be…
We discuss the role of the multiplicative anomaly for a complex scalar field at finite temperature and density. It is argued that physical considerations must be applied to determine which of the many possible expressions for the effective…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the…
We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting…
Thermal superspace is characterized by Grassmann variables which are time-dependent and antiperiodic in imaginary time, with a period given by the inverse temperature. The thermal superspace approach allows to define thermal superfields…