BRST-BFV formalism for the generalized Schwinger model

We derive the Wess-Zumino scalar term of the generalized Schwinger model both in the singular and nonsingular cases by using BRST-BFV framework. The photon propagators are also computed in the extended Lorentz gauge.     

A simple formalism for the BPS monopole

A simple formalism for the BPS monopole is obtained by generalizing the ADHM construction of multi-instantons to a Hilbert space. Both the potential itself and the Green's functions for different isospin can be obtained with very little effort from the instanton formulae.     

On the wavelet formalism for multifractal analysis

It is proved that the multifractal characterizations of diametrically regular measures that are provided by the wavelet and by the Hentschel-Procaccia formalisms are identical. (c) 2001 American Institute of Physics.     

On the thermodynamic formalism for the gauss map

We study the generalized transfer operator ? _β f(z)= \(\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{z + n}}} \right)^{2\beta } \times f\left( {1/\left( {z + n} \right)} \right)} \) of the Gauss mapTx=(1/x) mod 1 on the unit interval. This operator, which for β=1 is the familiar Perron-Frobenius operator ofT, can be defined for Re β>1/2 as a nuclear operator either on the Banach spaceA _∞(D) of holomorphic functions over a certain discD or on the Hilbert space ? _Reβ ⁽²⁾ (H _-1/2 of functions belonging to some Hardy class of functions over the half planeH _?1/2. The spectra of ? _β on the two spaces are identical. On the space ? _Reβ ⁽²⁾ (H _-1/2 ? _β is isomorphic to an integral operatorK _β with kernel the Bessel function \(\mathfrak{F}_{2\beta - 1} (2\sqrt {st} )\) and hence to some generalized Hankel transform. This shows that ? _β has real spectrum for real β>1/2. On the spaceA _∞(D) the operator ? _β can be analytically continued to the entire β-plane with simple poles atβ=β _k =(1-k)/2,k=0, 1, 2,..., and residue the rank 1 operatorN ^(k) f=1/2(1/K!)f ^(k)(0) . From this similar analyticity properties for the Fredholm determinant det (1-? _β ) of ? _β and hence also for Ruelle's zeta function follow. Another application is to the function \(\zeta _{\rm M} (\beta ) = \sum\limits_{n = 1}^\infty {\left[ n \right]^\beta } \) , where [n] denotes the irradional [n]=(n+(n ²+4)^1/2)/2.ζ _M (β) extends to a meromorphic function in the β-plane with the only poles at β=±1 both with residue 1.     

On the thermodynamic formalism for the Gauss map

We study the generalized transfer operator of the Gauss mapTx=(1/x) mod 1 on the unit interval. This operator, which for =1 is the familiar Perron-Frobenius operator ofT, can be defined for Re >1/2 as a nuclear operator either on the Banach spaceA (D) of holomorphic functions over a certain discD or on the Hilbert space of functions belonging to some Hardy class of functions over the half planeH _–1/2. The spectra of on the two spaces are identical. On the space is isomorphic to an integral operator with kernel the Bessel function and hence to some generalized Hankel transform. This shows that has real spectrum for real >1/2. On the spaceA (D) the operator can be analytically continued to the entire -plane with simple poles at and residue the rank 1 operator . From this similar analyticity properties for the Fredholm determinant of and hence also for Ruelle's zeta function follow. Another application is to the function , where [n] denotes the irrational[n]=(n+(n ²+4)^1/2)/2. M() extends to a meromorphic function in the -plane with the only poles at =±1 both with residue 1.     

Spin-rotation formalism for Meson-Baryon scattering

A spin-rotation formalism is developed for the extraction of physical quantities from the reaction π^- p↑→K°Λ, using the Λ-decay as polarisation analyser. The method described here uses the parameters polarisation,P, and spin-rotation angle, β. Effects due to apparatus acceptance are explicitly included. The method has advantages in minimising the sensitivity to various systematic errors.     

Scattering formalism for non-localizable fields

We consider the theory of a non-localizable relativistic quantum field. Nonlocalizability means that the field is not a tempered distribution, but increases strongly for large momenta. Local commutativity can then not be satisfied. Instead we assume the existence of Green's functions with the usual analyticity properties. We show that in such a theory theS-matrix can be defined, and its elements can be expressed in terms of the fields by the usual reduction formulae.     

Hamiltonian formalism for non-invariant dynamics

In a completely Hamiltonian dynamical system, there will be a generating functionH _Y for each infinitesimal space-time transformationY. In the non-autonomous case, theH _Y depend on the observer. This dependence is here described by a system of commutation relations. It is also shown that these relations can be made to mirror exactly the commutation relations of theY's in the Lorentz-invariant case.The preparation of this paper was supported in part by NSF grant GP-33696X. It is a pleasure to acknowledge discussions with Professor H. Bacri, D. Kastler, J. M. Souriau and others at CNRS, CPT, Marseilles.     

A Hamilton-Jacobi formalism for thermodynamics

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is 2n+1-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The ‘time’ variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.     

Covariant canonical formalism for gravity

We continue the previous discussion (A. D'Adda, J. E. Nelson, and T. Regge, Ann. Phys. (N.Y.)165) of the covariant canonical formalism for the group manifold and relate it to the standard canonical vierbein formalism as pioneered by Dirac. The form bracket is related to the Poisson bracket of classical mechanics. We utilise systematically the calculus of differential forms and a compound notation which labels Poincaré multiplets. In this way we obtain a particularly clear and compact expression for the Hamiltonian and the constraints algebra of the vierbein formalism.     

Slave fermion formalism for the tetrahedral spin chain

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.     

SUSY formalism for the symmetric double well potential

Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.     

Background formalism for superstring field theory

In the framework of the background formalism we analyse possible versions of the Witten-type NSR superstring field theory. We find the picture for string fields to be uniquely fixed by the requirement that the perturbative classical solutions are well-defined. This uniquely defined picture and the corresponding action are different from the ones in Witten's theory and coincide with the ones proposed from different reasons in our previous paper. Following the same background method we calculate the tree-level scattering amplitudes for the new action and argue that in contrast to the ones in Witten's original theory, the amplitudes are singularity-free and hence there is no need to add any tree-level counterterms. We also prove the amplitudes to reproduce correctly the first quantized results.