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We consider the large order behavior of the perturbative expansion of the scalar $\varphi^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order…
We propose a gauge invariant formulation of the effective potential in terms of a gauge invariant order parameter, for the Abelian Higgs model. The one-loop contribution at zero and finite temperature is computed explicitly, and the leading…
Starting from a theory of heavy particles and antiparticles, the path integral formulation of an effective field theory which describes the low momentum interactions is presented. The heavy degrees of freedom are identified and explicitly…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the…
We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A…
The Fock-Schwinger proper-time method is used to derive the effective action in the field theory with the chiral $U(3)\times U(3)$ symmetry explicitly broken by unequal masses of heavy particles. The one-loop effective action is presented…
The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the…
One-loop amplitudes may be expanded in a basis of scalar integrals multiplied by rational coefficients. We relate the coefficient of the one-point integral to the coefficients of higher-point integrals, by considering the effects of…
The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…
The method of the large mass expansion (LME) is investigated for selfenergy and vertex functions in two-loop order. It has the technical advantage that in many cases the expansion coefficients can be expressed analytically. As long as only…
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
The motion of a small compact object (SCO) in a background spacetime is investigated further in a class of model nonlinear scalar field theories having a perturbative structure analogous to the General Relativistic description of extreme…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
The coefficients appearing at leading and subleading order in the $1/m$ expansion of bilinear heavy quark currents are related to each other by imposing reparametrization invariance on both the effective current operators and the…
Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with…
A Carleman Weight Function (CWF) is used to construct a new cost functional for a Coefficient Inverse Problems for a hyperbolic PDE. Given a bounded set of an arbitrary size in a certain Sobolev space, one can choose the parameter of the…
In this work, we mainly study the one-loop effective action for real scalar theories in non-homogeneous backgrounds in odd dimensions. It is shown that through the method studied in Ref. [1], it is possible to obtain a unified result for…
We derive a new kind of recursion relation to obtain the one-particle-irreducible (1PI) Feynman diagrams for the effective action. By using this method, we have obtained the graphical representation of the four-loop effective action in case…