Related papers: Computing numerically the functional derivative of…
On the basis of a new approach proposed in our previous work we develope a formalism for calculating of the effective action for some models containing fermion fields. This method allows us to calculate the fermionic part of the effective…
New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
We use a functional approach to study various aspects of the quantum effective dynamics of moving, planar, dispersive mirrors, coupled to scalar or Dirac fields, in different numbers of dimensions. We first compute the Euclidean effective…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem,…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An…
The derivative expansion of the one-loop effective action in QED$_3$ and QED$_4$ is considered. The first term in such an expansion is the effective action for a constant electromagnetic field. An explicit expression for the next term…
The second functional derivative of the effective potential of pure fermionic field theories is rewritten in a factorized form which facilitates the evaluation of the renormalisation flow rate of the effective action in the Wetterich…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
The effective equation of motion is derived for a scalar field interacting with other fields in a Friedman-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in…
A method for determining the leading quantum contributions to the effective action for both zero and finite temperatures is presented. While it is described in the context of a scalar field theory, it can be straight-forwardly extended to…
An indication of spontaneous symmetry breaking is found in the two-dimensional $\lambda\phi^4$ model, where attention is paid to the functional form of an effective action. An effective energy, which is an effective action for a static…
I compute the derivative expansion of an effective action at finite temperature using the imaginary time approach. I show that it is a well behaved expansion giving a unique seriers contrary to previous results. This disparity is shown to…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective…