Irrelevant operators and momentum-shell recursion relations ind=2 + ∈ dimensions

The momentum-shell recursion relations of Nelson and Pelcovits for ann-vector model near two dimensions are reexamined. The renormalization of the infinite set of relevant and marginal operators present in the system is studied. Ambiguities obtained in the ensuing recursion relations are shown to involve irrelevant operators only, thus justifying the procedure of Nelson and Pelcovits. The cases of finite external fieldh and finite spin anisotropyg are both considered.     

Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.     

Variational study of vacuum structure with fermions ind+1 dimensional Hamiltonian lattice gauge theory

The physical vacuum state and general expression for the Hamiltonian ofd+1 dimensional lattice gauge theory are given by incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state. The applications toSU(2) andSU(3) gauge theories in 2+1 and 3+1 dimensions are demonstrated and the fermion condensates \(\left\langle {\bar \psi \psi } \right\rangle \) as functions of 1/g ² are calculated.     

Hamiltonian formulation of d = 10 supergravity theories

A method is given for deriving the hamiltonian form of the d = 10 supergravity models. It is explicitly applied to the N = 1 theory.     

Hamiltonian formulation for the positron trapping model

Summary A Hamiltonian formulation is used to build up an adequate Hamiltonian for the positron trapping model. The number of positrons annihilated in the free state,n _f, or the trapped one,n _v, are considered canonical conjugate variables; this point of view provides a route to propose a Hamiltonian which leads to the previously proposed phenomenological master equations.

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Riassunto Si usa una formulazione hamiltoniana per elaborare un'hamiltoniana adeguata per il modello a trappola dei positroni. Il numero di positroni annichilati nello stato libero,n _f, o in quello intrappolato,n _v, è considerato come variabili coniugate canoniche; in questo senso si fornisce una via per proporre un'hamiltoniana che porti alle equazioni principali fenomenologiche proposte precedentemente.

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Резюме Гамильтонова формулировка используется для конструирования адекватного Гамильтониана для модели захвата позитрона. Число аннигилированных позитронов в свободном состоянии,n _f, или число захваченных позитронов,n _v, рассматриваются как канонически сопряженные переменные. Этот подход приводит к Гамильтониану. Который дает ранее предположенные феноменологические ?управляющие? уравнения.

     

Hamiltonian formulation of the anomalous chiral Schwinger model

We construct the hamiltonian formulation of the anomalous chiral Schwinger model, which has recently been shown to yield a consistent unitary theory. The impact of the anomaly on the constraints of the system is exhibited and the system is quantized using an appropriate hamiltonian consistent with the constraints.     

N = 1 superstring in 2 + 2 dimensions

In this paper we construct a (2,2) dimensional string theory with manifest N = 1 spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The worldsheet symmetry algebra is a twisted and truncated “small” N = 4 superconformal algebra. The realisation of the symmetry algebra is reducible with an infinite order of reducibility. We study the physical states of the theory by two different methods. In one of them, we identify a subset of irreducible constraints, which is by itself critical. We construct the BRST operator for the irreducible constraints, and study the cohomology and interactions. This method breaks the SO(2,2) spacetime symmetry of the original reducible theory. In another approach, we study the theory in a fully covariant manner, which involves the introduction of infinitely many ghosts for ghosts.     

Solution for the null-surface formulation of general relativity in 2+1 dimensions

We study the Schwarzschild and Reissner-Nordström black hole thermodynamics using the simplest form of the generalized uncertainty principle (GUP) proposed in the literature. The expressions for the mass-temperature relation, heat capacity and entropy are obtained in both cases from which the critical and remnant masses are computed. Our results are exact and reveal that these masses are identical and larger than the so called singular mass for which the thermodynamics quantities become ill-defined. The expression for the entropy reveals the well known area theorem in terms of the horizon area in both cases upto leading order corrections from GUP. The area theorem written in terms of a new variable which can be interpreted as the reduced horizon area arises only when the computation is carried out to the next higher order correction from GUP.     

Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions

We develop a theory of integrable dispersive deformations of 2+1 dimensional Hamiltonian systems of hydrodynamic type following the scheme proposed by Dubrovin and his collaborators in 1+1 dimensions. Our results show that the multi-dimensional situation is far more rigid, and generic Hamiltonians are not deformable. As an illustration we discuss a particular class of two-component Hamiltonian systems, establishing the triviality of first order deformations and classifying Hamiltonians possessing nontrivial deformations of the second order.     

A study of the generalized Schwinger model in the Hamiltonian formulation

Semileptonic τ decays to two and three pions are considered. Based on recent data for the pion form factor a new prediction for Γ(τ→vπ^{- 0})/Γ(τ→vev_e) of 1.32±0.05 is derived. The chiral model-supplemented by vector dominance-is used to predict rate and differential distributions for the three pion mode in good agreement with present data. The parity violating asymmetry which has been predicted theoretically and observed experimentally is studied and found to be fairly insensitive towards the details of the model for the hadronic decays.     

Hamiltonian formulation of the supermembrane

The hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence-free 2-vectors are unfixed.     

Structure ofN=1 conformal and Poincaré supergravity in 1+1 and 2+1 dimensions

We discuss a component formalism ofN=1 supergravity theories in 2 and 3 spacetime dimensions. Starting from gauge theories of the superconformal group, we derive the tensor calculus for conformal and Poincaré supergravity theories. A supersymmetric extension of the non-trivial analog of Einstein's equation for 2 dimensions is given in terms of the scalar curvature multiplet.     

A stochastic model of Maxwell's equations in 1+1 dimensions

We show that the random walk model due to Mark Kac which underlies the telegraph equations may be modified to produce Maxwell's field equations in 1+1 dimensions. This provides the field equations with a representation in terms of classical particles. It also establishes the Kac model as a strong conceptual link between the diffusion, telegraph, and Maxwell equations, and suggests that recent simulations of the Schrödinger and Dirac equations are analogous to Maxwell's equation in terms of interpretation.