Canonical Transformations in a Higher-Derivative Field Theory

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiral-gauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.Comment: 12 pages, LaTe

Decoupled path integral formulation of chiral QCD2_2 with aJR=2a_{JR}=2

We analyse the BRST constraints and corresponding Hilbert-space structure of chiral QCD$_2$ in the decoupled formulation for the case of the Jackiw-Rajaraman parameter $a=2$. We show that despite formal similarities this theory is not equivalent to QCD$_2$, and that its extension to U(N) does not lead to an infinite vacuum degeneracy.Comment: LaTeX, 22 page

Structural Aspects of Two-Dimensional Anomalous Gauge Theories

A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the fundamental set of field operators whose Wightman functions define the model. We examine the effect of the use of a redundant field algebra in deriving basic properties of the models and show that different results may arise, as regards the physical properties of the generalized chiral model, in restricting or not the Hilbert space as representation of the intrinsic local field algebra. The question referring to considering the vector Schwinger model as a limit of the generalized anomalous model is also discussed. We show that this limit can only be consistently defined for a field subalgebra of the generalized model.Comment: 40 pages. Latex, to appear in Annals of Physic

Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

Decoupled Path Integral Formulation of Chiral QCD2withaJR=2

We analyse the BRST constraints and corresponding Hilbert-space structure of a chiral QCD2in the decoupled formulation for the case of the Jackiw-Rajaraman parametera=2. We show that despite formal similarities this theory is not equivalent to QCD2, and that its extension toU(N) does not lead to an infinite vacuum degeneracy. © 1998 Academic Press.Articl

Canonical quantization of nonlocal theories related to bosonization in 2+1D

Work partially supported by SCT/PR, CAPES and CNPqSIGLEITItal