Higher-derivative Field Theories Research Articles

Bound-state gravity from higher derivatives

In certain Lorentz-covariant higher-derivative field theories of spins ⩽1, would-be ultraviolet divergences generate color-singlet poles as infrared divergences. Absence of higher-order poles implies ten-dimensional supersymmetric Yang–Mills with bound-state supergravity, in close analogy with open-string theory.

Quantization of higher-derivative field theories

A free-scalar field satisfying a wave equation with any number of time derivatives is expanded in terms of creation and annihilation operators that are quantized by replacing the classical Poisson brackets of Ostrogradski by the commutator. Regardless of the coefficients in the wave equation, various algebraic identities make it possible to explicitly carry out the quantization, construct the Hamiltonian, and evaluate the propagator. There are always states of negative norm. A wave equation whose highest time derivative is order 2 N can have N single-particle states with positive, real energy. Of these, the number of negative-norm states will be N/2 if N is even and ( N−1)/2 if N is odd.

Field algebra, Hilbert space and observables in two-dimensional higher-derivative field theories

We discuss structural aspects related to the field algebra of two-dimensional higher-derivative quantum field theories. We present general selection criteria for the proper field subalgebra that generates Wightman functions satisfying the asymptotic factorization property and which define a semi-definite inner product Hilbert space. The positive definite inner product Hilbert space, which contains as a subspace of states the general Wightman functions of the corresponding standard canonical models, is a quotient space obtained by equivalence classes. For higher-derivative local gauge theories, besides the Lowenstein–Swieca condition, an additional condition must be imposed on the field algebra in order to obtain a physical subspace of states satisfying a reasonable set of physically meaningful axioms.

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 chiralgauge 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.

Nontrivial fixed point in the 4D Φ4 lattice model with internal O(N) symmetry

It is shown that the infinite dimensional critical surface of general euclidean lattice actions in a generic four-dimensional scalar field theory with $\Phi^4$ interactions has a domain of special multicritical points where higher dimensional operators play a special role. Renormalized trajectories of higher derivative continuum field theories with nontrivial interactions are traced back to special ultraviolet stable fixed points on the manifold of multicritical points. These fixed points have an infinite number of relevant directions which identify the universality classes of critical higher derivative field theories. The relevance of the new fixed point structure is discussed within the context of the triviality Higgs mass bound.

Gauge fixing in higher derivative field theories

Higher derivative (HD) field theories can be transformed into second order equivalent theories with a direct particle interpretation. In a simple model involving abelian gauge symmetries we examine the fate of the possible gauge fixings throughout this process. This example is a useful test bed for HD theories of gravity and provide a nice intuitive interpretation of the “third ghost” occuring there and in HD gauge theories when a HD gauge fixing is adopted.

On the canonical structure of higher-derivative field theories. The gravitational WZW-model

A general expression for the symplectic structure of a higher-derivative lagrangian field theory is given. General relativity and the gravitational WZW-model are considered in this framework. In the second case we work out explicitly the Poisson bracket for both chiral solutions giving rise, in two different ways, to the classical exchange algebra of the SL q (2) group.

Off-shell d=10, N=1 Poincaré supergravity and the embeddibility of higher-derivative field theories in superspace

The constraints on the supertorsion are presented which lead to off-shell d=10, N=2 Poincaré supergravity and the superfluids which are known to enter the superspace action are identified. It is pointed out that Poincaré off-shell constraints have to be used in a superspace formulation of the low-energy effective actions of N=1 superstrings. However, current formulations of N=1 superstrings propagating in arbitrary supergravity backgrounds are incompatible with these off-shell constraints.

Counting of states in higher-derivative field theories

A canonical approach shows that conformal gravitons have six states and conformal gravitinos have eight states. These results differ from previous counts which yielded four and six states, respectively, and solve a puzzle in $N=2$ extended conformal supergravity. They agree with results of Fradkin and Tseytlin based on a path-integral approach.