we review various ways to express the partition function of the single-band hubard model as a path integral. the emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly.   since the single-band hubbard model is a pure fermionic model on the lattice and its hamiltonian is a polynomial in creatio...

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. A comparison with density functional theory (DFT) and second-order Moller-Ples...

Using path integral method (Fujikawa’s method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representation. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit p̃μ(≡ θpν) → 0. The adjoint chiral fermion carries no anomaly in non-planar sector in D = 4k(k ...

We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the wave speed, with amplitude that is slowly changing depending on the medium coefficients, under t...

Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the statistical properties of the data can be modelled by a multivariate Gaussian distribution. We use this to show how one can optimise an experiment to find evid...

Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2) q , we construct path integral representation for the quantum mechanical evolution operator kernel of q-oscillator.