Renormalization of the Wess-Zumino model with a nonminimal coupling to an external supergravity field

The renormalization structure of the parameters corresponding to nonminimal coupling between a scalar superfield and an external supergravity field is studied. The renormalization group equations are obtained for the corresponding effective charges, and their asymptotic behavior is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 62–68, July, 1988.     

Low-energy constraints on supergravity parameters

We make a careful analysis of the constraints on supergravity parameters from the requirement of SU(2)×U(1) symmetry breaking. Since we obtain fully analytic solutions to the relevant renormalization group equations, we are able to explore the whole range of parameters. Breaking electroweak symmetry with a light top quark leads to a strong correlation between the dimensionless parameters and the mass ratios in the supergravity lagrangian. However, the overall mass scale, e.g. $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, is not fixed by this requirements. The bound on the lightest neutral Higgs boson is reexamined. The lightest squark is usually an s-top, but we easily find cases where it is a s-bottom. Unfortunately the low-energy constraints provide no useful guidelines for experimentalists.     

Cosmological constraints on supergravity models

We delineate the domain of supersymmetry breaking parameters in minimal supergravity models for which the cosmological relic photino density is no larger than the closure density. Demanding that the relic density equal the closure density as suggested by inflationary cosmology suggests $\text{m}{}_{\mathrm{<mtext>q</mtext><mtext>?</mtext>}}\text{～ 42}\text{GeV}\text{+ 0.89 m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}$. We point out that several supergravity scenarios for the monojet events at the CERN $\text{p}$p Collider would yield a relic density considerably greater than the closure density.     

Quantum Hamiltonian formalism with constraints

A quantum system with constraints that does not necessarily correspond to a classical system with constraints is described in the Hamiltonian formalism.     

Hamiltonian formalism,quantization and S matrix for supergravity

The canonical formalism for supergravity is constructed. The algebra of canonical constraints is found. The correct expression for the S matrix is obtained. Usual “covariant methods” lead to an incorrect S matrix in supergravity, since a new four-particle interaction of ghostfields survives in the Lagrangian expression of the S matrix.     

The supergroup manifold formulation of the Wess-Zumino multiplet revisited: The supercurrent and the supergravity auxiliary fields

In this paper we provide a consistent first-order group-manifold formulation of the Wess-Zumino system. It is shownhow the well-known auxiliary fields of the ($\text{1}\text{2}$, 0, 0) system arise by supplementing Bianchi identities with the “second-order constraints”; that is, those equations allowing the transition from the first order to the second order of the theory. When the ($\text{1}\text{2}$, 0, 0) multiplet is coupled to N = 1 supergravity and the torsion “second-order constraint” is implemented, we get a non-minimal set of auxiliary fields (scalar, pseudoscalar axial vector and a spinor). We argue this to be the fundamental set of auxiliary fields. The so-called “minimal set” is not coordinate invariant and can be recovered only by adding a non-geometrical constraint.     

Canonical formalism of gauge theories with reducible constraints

A procedure for the canonical quantization of gauge theories with reducible constraints (that is, linearly dependent) is proposed. The procedure consists of extending the initial phase space and filling out the initial system of constraints to an aggregate of linearly indepndent constraints. The equivalence is shown between the proposed quantization scheme and canonical quantization when only the linearly independent constraints are chosen from the initial system of constraints.Translated from Izvestiya Vysshikh.Uchebnykh Zavedenii, Fizika, No. 7, pp. 64–68, July, 1985.     

Algebraic derivation of N = 2 supergravity constraints

A purely algebraic derivation is given of the superspace constraints of N = 2 extended supergravity. The derivation proceeds through an analysis of the integrability conditions needed to preserve the irreducible representations of rigid N = 2 supersymmetry, taking account of the local complex dilation and SU(2) invariances of the constraints.     

A complete solution of the Bianchi identities in superspace with supergravity constraints

A short discussion of the superspace formulation of supergravity is given and the Bianchi identities are derived. The supergravity constraints are imposed and the identities are solved in terms of superfields and their covariant derivatives.     

On the problem of spacetime symmetries in the theory of supergravity. III. Superspace formalism

The study of the problem of defining, in the theory of supergravity, the notion of a spacetime symmetry is continued. The connection with the formalism of superspace is explicitly considered, and the geometrical significance of the definition given in Parts I and II of this series of papers is emphasized.     

Simplification of the constraints in the dirac formalism for general relativity

In any classical theory in canonical form, the Poisson bracket relations between the constraints are preserved under canonical transformations. We show that in the Dirac formalism for general relativity this condition places certain limits on the degree to which one can simplify the form of the constraints. It implies, for instance, that the constraints cannot all be written as canonical momenta. Furthermore, it is not even possible to reduce them all to purely algebraic functions of the momenta by means of a canonical tansformation which preserves the original configuration space subspace of phase space.     

Simplification of the constraints in the dirac formalism for general relativity

In any classical theory in canonical form, the Poisson bracket relations between the constraints are preserved under canonical transformations. We show that in the Dirac formalism for general relativity this condition places certain limits on the degree to which one can simplify the form of the constraints. It implies, for instance, that the constraints cannot all be written as canonical momenta. Furthermore, it is not even possible to reduce them all to purely algebraic functions of the momenta by means of a canonical tansformation which preserves the original configuration space subspace of phase space.