Related papers: Computing numerically the functional derivative of…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field…
It is shown that the functional determinant ($\sim$ effective action) for a scalar field propagating on the mixed signature product of unit spheres, S$^q\times$S$^p$, according to the GJMS operator, depends, if $d$ is odd, only on $d=p+q$…
Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this…
The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in…
Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time,…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
In this paper we calculate the effective action for neutral particles with anomalous magnetic moment in an external magnetic and electric field. We show that we can take advantage from the Foldy Wouthuysen transformation for such systems,…
We analyse the one-loop fermionic contribution for the scalar effective potential in the temperature dependent Yukawa model. In order to regularize the model a mix between dimensional and analytic regularization procedures is used. We find…
We consider a scalar field theory with quartic self interaction, Yukawa coupled to fermions in the inflationary de Sitter spacetime background. The scalar has a classical background plus quantum fluctuations, whereas the fermions are taken…
We work with $\phi^4$ theory and study the 4PI effective action at 3-loop order. We discuss the relationship between the equations of motion obtained by taking functional derivatives of the effective action with respect to the variational…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
This article describes the fuzzy conformable fractional derivative which is based on generalized Hukuhara differentiability. On these topics, we prove a number of properties concerning this type of differentiability. In addition, fuzzy…
We estimate the effects of dynamical fermions by extrapolating to positive flavour numbers the results from negative values obtained by adding to the pure gauge sector a fermion action where the fields obey a Bose statistics: the bermions.
We carefully analyse the use of the effective action in dynamical problems, in particular the conditions under which the equation $\frac{\delta \Ga} {\delta \phi}=0$ can be used as a quantum equation of motion, and the relation between the…
We pursue further an approach to lattice chiral fermions in which the fermions are treated in the continuum. To render the effective action gauge invariant, counterterms have to be introduced. We determine the counterterms for smooth gauge…
We derive the fermionic contribution to the 1-loop effective action for A_4 and A_i fields at high temperatures, assuming that gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4.