Path - integral Evidence

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  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 creat...

Numerical solution of higher index DAEs using their IAE's structure: Trajectory-prescribed path control problem and simple pendulum

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

Path Integral Monte Carlo Simulations for Fermion Systems : Pairing in the Electron - Hole Plasma

We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of " ring-polymers " and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to possible " cross-linking " of polymers. As proposed by Feynman, superfluidity and Bose condensation result from macroscopic exchange of bosons. To map fermions on...

Behavioral and electrocortical evidence of distinct reference frames supporting path integration

Regge’s space-time skeletons and the quantization of 2d gravity

One possibility to quantize gravity is to focus on finding a regularization of the euclidean path integral. Most studies so far have used either the dynamical triangulation (DT) or the Regge approach (RA). The continuum path integral is replaced in both cases by a summation over simplicial manifolds (skeletons). In the RA the edge lengths are the dynamical degrees of freedom and the connectivit...