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Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
Tunneling in quantum field theory is worth understanding properly, not least because it controls the long term fate of our universe. There are however, a number of features of tunneling rate calculations which lack a desirable transparency,…
Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two…
Path integral Monte Carlo with Green's function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path…
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 use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
We propose a new method to evaluate the effective potential in the path integral for the fixed-energy amplitude as well as for the pseudotime evolution kernel in the formalism by Duru and Kleinert. Restriction to the postpoint or the…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing…
A Wiener-regularized path integral is presented as an alternative way to formulate Berezin-Toeplitz quantization on a toroidal phase space. Essential to the result is that this quantization prescription for the torus can be constructed as…
In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering…
The tunneling rate, with exact prefactor, is calculated to first order in \hbar for a closed FRW universe filled with perfect fluid violating the strong energy condition. The calculations are performed by applying the dilute-instanton…
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…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem…
We impose the periodicity conditions corresponding to the Matsubara formalism for Thermal Field Theory as constraints in the imaginary time path integral. These constraints are introduced by means of time-independent auxiliary fields which,…
We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, $V(x)=x^2/2-gx^4/4$. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part…
We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…