Related papers: On the total derivative divergence for a nonminima…
The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory…
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We…
We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…
The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
The trace of the heat kernel and the one-loop effective action for the generic differential operator are calculated to third order in the background curvatures: the Riemann curvature, the commutator curvature and the potential. In the case…
We prove that if $H$ denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph $(X,b,m)$, and if $v:X\to \mathbb{R}$ is such that $H+v/\hbar$ is well-defined as a form sum for all…
The quantization of Einstein-Maxwell theory with a cosmological constant is considered. We obtain all logarithmically divergent terms in the one-loop effective action that involve only the background electromagnetic field. This includes…
We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration…
We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the $N$-particle relativistic Toda chain and test our proposal against…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
In a previous study it was demonstrated that Dirac's relativistic quantum equation for free electrons (DRQM)can be obtained from Maxwell's classical electromagnetic field equations (MaxEq). This raises fundamental issues about the…
We consider the harmonic superspace formulation of higher-derivative $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with the decreasing one-parameter family of translated standard subspaces is convex for any given (not necessarily smooth) vector in…
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
Using the generalized Schwinger-DeWitt technique, we calculate the divergent part of the one-loop effective action for gravity non-minimally coupled to a multiplet of scalar fields. All the calculations are consistently done in the Jordan…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…