Related papers: Computing numerically the functional derivative of…
We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary…
We consider macroscopic motion of quantum field systems. Zubarev statistical operator allows to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of…
We consider the theory of four-fermion interactions with N-component fermions in de Sitter space. It is found that the effective potential for a composite operator in the theory is calculable in the leading order of the 1/N expansion. The…
Chapter one is devoted to a study of fermions and bosons in two spatial dimensions in external electromagnetic fields. The effectve action is calculated by integrating out the matter fields. In chapter two, I investigate the resummation…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
This study investigates the nth-level Prabhakar fractional derivative, a generalization encompassing some well-known fractional derivatives. We establish its fundamental properties, particularly its relationship with the corresponding…
We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function…
Building on previous developments, we show that the Diagrammatic Monte Carlo technique allows to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting…
A simple systematic method for calculating derivative expansions of the one-loop effective action is presented. This method is based on using symbols of operators and well known deformation quantization theory. To demonstrate its advantages…
We present the fermionic universal one--loop effective action obtained by integrating out heavy vector--like fermions at one loop using functional techniques. Even though previous approaches are able to handle integrating out heavy fermions…
Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule.…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
A functional partial differential equation is set for the proper graphs generating functional of QED in external electromagnetic fields. This equation leads to the evolution of the proper graphs with the external field amplitude and the…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
We consider a higher derivative effective theory for an Abelian gauge field in three dimensions, which represents the result of integrating out heavy matter fields interacting with a classical gauge field in a parity-conserving way. We…
In a four dimensional theory of gravity with lagrangian quadratic in curvature and torsion, we compute the effective action for metrics of the form $g_{\mu\nu}=\rho^2\delta_{\mu\nu}$, with $\rho$ constant. Using standard field-theoretic…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
The traditional first approach to fractional calculus is via the Riemann-Liouville differintegral $_{a}D_{x}^{k}$. The intent of this paper will be to create a space $K$, pair of maps $g: C^{\omega}(\mathbb{R}) \to K$ and $g': K \to…
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…