Related papers: A note on the functional determinant of higher-der…
We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We…
In this paper, we introduce a new operator, $\mathcal{S}$, which is closely related to the restriction problem for spheres in $\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. The…
The spectral action on the equivariant real spectral triple over \A(SU_q(2)) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of…
We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production…
A general method of finding functional determinants is presented that depends on the asymptotic behaviour of the resolvent. Its application to the case of a bounded trihedral corner for which the eigenvalues are known only implicitly is…
We address the computation of the determinant for the Dirac operator corresponding to a quark propagating in a background gluon field of the following type: the gauge field is covariantly constant and self-dual inside a hypersphere and with…
We discuss the role that higher derivative operators play in field theory orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz) breaking of supersymmetry. Integrating out the bulk fields generates brane-localised…
We calculate the effective action for a constant magnetic field and a time-dependent time-component of the gauge field in 2+1 dimensions at finite temperature. We also discuss the behaviour of the charge density and the fermion condensate…
We show that the action of a dynamical system can be supplemented by an effective action for its environment to reproduce arbitrary coordinate dependent ohmic dissipation and gyroscopic forces. The action is a generalization of the harmonic…
The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental {\pi}…
We calculate the effective potentials for scalar, Dirac and Yang-Mills fields in curved backgrounds using a new method for the determination of the heat kernel involving a re-summation of the Schwinger-DeWitt series. Self-interactions are…
We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined…
Let A -> B be a homomorphism of commutative rings. The squaring operation is a functor Sq_{B/A} from the derived category D(B) of complexes B-modules into itself. The squaring operation is needed for the definition of rigid complexes (in…
Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables. In this paper, we present explicit expressions for zonal functions of de Sitter…
We study the effects of a uniform magnetic field on the one-dimensional spin-orbital model in terms of effective field theories. Two regions are examined: one around the SU(4) point (J=K/4) and the other with K<<J. We found that when $J\leq…
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and…
We study the small mass limit of the one-loop spinor effective action, comparing the derivative expansion approximation with exact numerical results that are obtained from an extension to spinor theories of the partial-wave-cutoff method.…
It is shown how operator regularization can be used to obtain an expansion of the effective action in powers of derivatives of the background field. This is applied to massless scalar electrodynamics to find the one-loop corrections to the…
Let $D(s)$ be a fractional derivation of order $s$. For a real $p\ne 0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p) D(s) A(p)^{-1}=D(p s)$ for all $s$. The kernel of the operator $A(p)$ is…
Configuration space heat-kernel methods are used to evaluate the determinant and hence the effective action for an SU(2) doublet of fermions in interaction with a {\it covariantly constant} SU(2) background field. Exact results are…