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We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a…
In this paper, we study the one-loop effective potential of a derivative four-fermion model. As a result, an exact bumblebee-like potential is radiatively generated. Afterwards, we generalize our study for a finite temperature case and…
Two different theoretical formulations of the finite temperature effects have been recently proposed for integrable field theories. In order to decide which of them is the correct one, we perform for a particular model an explicit check of…
The analytic properties in the energy variable k_{0} of finite-temperature self-energies are investigated. A typical branch cut results from n particles being emitted into the heat bath and n' being absorbed from the heat bath. There are…
The conventional results for hard thermal loops, which are the building blocks of resummed perturbation theory in thermal field theories, have collinear singularities when external momenta are light-like. It is shown that by taking into…
We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-countable, linearly topologized rings, and actions of the…
The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge-dependence of the effective potential.…
We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of…
We prove that a functional with Lipschitzian derivative, when restricted to suitable spheres centered at a noncritical point, has a unique maximum.
In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that even at concentrations beyond the…
We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide…
Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables…
Through the application of the thermal operator to the zero temperature retarded Green's functions, we derive in a simple way the well known hard thermal effective action in QCD. By relating these functions to forward scattering amplitudes…
We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\Omega(\tilde{\mu})$ with complex chemical potential $\tilde{\mu}$. The result is given in terms of a single sum the coefficients of…
Analytic expressions for the $N$-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.
We provide convincing empirical evidence that long range interactions strongly enhance the rectification effect which takes place in mass graded systems. Even more importantly the rectification does not decrease with the increase of the…
We consider two approaches to calculate imaginary parts of effective actions in expanding space-times. While the first approach uses Bogolyubov coefficients, the second one uses the functional integral or the Feynman propagator. In…