The character table of the double group of the icosahedral group, Ih 2 is derived. The correlation table for the rovibronic states as well as spin states both involving integral and half-integral spins are derived. It is shown that the spin states that correspond to half-integral and integral spins exhibit a cyclicity of 15 and 30, respectively, with respect to correlation into the double group...

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solito...

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...

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a 'fre...

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L functions on three-dimensional hyperbolic space. To ‘evaluate’ such a ...

We present a coherent picture of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz invariant local Lagrangian, when combined with Green’s functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman’s m−iǫ prescription ensures the positive energy condition regardless of statistics, and the abnorma...

We outline three new ideas in a program to obtain standard physics, including standard supersymmetry, from a Planck-scale statistical theory: (1) The initial spin 1/2 bosonic fields are transformed to spin 0 fields together with their auxiliary fields. (2) Time is defined by the progression of 3-geometries, just as originally proposed by DeWitt. (3) The initial (D-1)-dimensional “path integral”...

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H eff ({S i }) derived from the coherent-state integral is highly singular: the quasiprobability density exp(−βH eff), a Wigner function, imposes quantisation through derivatives of delta f...

The spin can be described in the star product formalism by extending the bosonic Moyal product in the fermionic sector. The fermionic star product is then the Clifford product of geometric algebra and it is possible to formulate the fermionic star product formalism in analogy to the bosonic star product formalism. For the fermionic star product description of spin, one can then establish the re...