Related papers: Augmenting the residue theorem with boundary terms…
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to…
Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation…
In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically…
We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing…
Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation…
We examine a very simple model for which the leading contribution to the one-loop effective potential at finite temperature is uniquely defined despite the presence of the Landau terms. In addition we report on the usual non-analyticity at…
We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the…
A very small amount of K\"ahler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian and polar coordinates, largely replacing the concept of…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal…
We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form…
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop…
In a thermal field theory, the cumulants of the momentum distribution can be extracted from the dependence of the Euclidean path integral on a shift in the fields built into the temporal boundary condition. When combined with the Ward…
The equations of time-dependent density functional theory are derived, via the expression for the quantum weak value, from ring polymer quantum theory using a symmetry between time and imaginary time. The imaginary time path integral…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
We introduce the boundary conditions corresponding to the imaginary-time (Matsubara) formalism for the finite-temperature partition function in $d+1$ dimensions as {\em constraints} in the path integral for the vacuum amplitude (the…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
We use a generalised real-time path formalism with properly regularised propagators based on Le Bellac and Mabilat \cite{belmab} and calculate the effective potential and the higher order derivative terms of the effective action in the case…
Recently, the spectral expansion of finite temperature two-point functions in integrable quantum field theories was constructed using a finite volume regularization technique and the application of multidimensional residues. In the present…
We discuss subtleties in the calculation of loop integrals in studies of hot and dense systems as they appear in both perturbative and non-perturbative approaches. To be specific, we address subtleties which appear in situations where the…