M.B. Halpern

Supersymmetric ground state wave functions

Abstract The construction of explicit supersymmetric ground states is considered in a variety of quantum mechanical systems. For broad classes of supersymmetric hamiltonians it is not difficult to find closed-form zero-energy ground-state wave functions.

STABILIZING BOTTOMLESS ACTION THEORIES

Abstract We show how to construct the euclidean quantum theory corresponding to classical actions which are unbounded from below. Our method preserves the classical limit, the large- N limit, and the perturbative expansion of the unstabilized theories.

Explicit spontaneous breakdown in a dual model (II). n-point functions

Abstract We continue the program of spurion summation in dual models. Starting from the propagator found in the first paper of this name, we develop sufficient technique to construct the final n-point functions.

Asymptotic Search for Ground States of SU(2) Matrix Theory

We introduce a complete set of gauge-invariant variables and a generalized Born–Oppenheimer formulation to search for normalizable zero-energy asymptotic solutions of the Schrodinger equation of SU(2) matrix theory. The asymptotic method gives only ground state candidates, which must be further tested for global stability. Our results include a set of such ground state candidates, including one state which is a singlet under spin (9).

Quenched master fields

Abstract We derive an exact algebraic (master) equation for the euclidean master field of any large- N matrix theory, including quantum chromodynamics. The master equation is the quenched Langevin equation. The master field, a translationally covariant function of (uniform) random momenta and (gaussian) random noise, is easily constructed in perturbation theory.

Continuum regularization of quantum field theory: (I). Scalar prototype

Abstract This paper, I, is the first in a series of papers in which we present a new, presumably nonperturbative, regularization scheme for continuum quantum field theory. The higher covariant derivative method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. We will discuss gauge theories explicitly in II. This first paper on scalar field theory is designed partly as a pedagogical vehicle to introduce the reader, in the simplest possible context, to the relevant regularized Langevin and regularized Schwinger-Dyson techniques — which extend more or less directly to gauge theory. The scalar context is also the simplest in which to study the curious feature that our scheme is not an action regularization, a fact which is crucial to its success in regulating theories with local symmetries. A renormalization program is checked through one loop, including a computation of the β-function in φ63.

Continuum regularization of quantum field theory: (III). The QCD4 β-function

Abstract A Schwinger-Dyson renormalization program is formulated for continuum-regularized QCD 4 . Ward identities are verified at one loop, and the usual one-loop β-function is obtained.

Continuum regularization of quantum field theory (II). Gauge theory

Abstract Following a recent letter, and a study of the scalar prototype in I, this paper discusses our new covariant-derivative regularization in the case of d -dimensional gauge theory. Details are given both at the ( d + 1)-dimensional stochastic level and at the d -dimensional level of the regularized Schwinger-Dyson equations. The regularized formulation is gauge-covariant, manifestly Lorentz invariant, ghost-free, and ultraviolet finite to all orders.

New unitary affine-Virasoro constructions

We report a quasi-systematic investigation of the Virasoro master equation. The space of all affine-Virasoro constructions is organized by K-conjugation into affine-Virasoro nests, and an estimate of the dimension of the space shows that most solutions await discovery. With consistent ansatze for the master equation, large classes of new unitary nests are constructed, including 1) quadratic deformation nests with continuous conformal weights, and 2) unitary irrational central charge nests, which may dominate unitary rational central charge on compact g.

Large N saddle formulation of quadratic building block theories

Abstract I develop a large N saddle point formulation for the broad class of “theories of quadratic building blocks”. Such theories are those in which the sums over internal indices are contained in quadratic building blocks, e.g., φ2 = Σa = 1N φa φa. The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N.