Non-covariant Formalism Research Articles

Polarization in (quasi-)two-body decays and new physics

We consider two-body and quasi-two-body decays of the type f_1 rightarrow f_2 B, where f_1 and f_2 are spin-1/2 fermions and B a spin-0 or spin-1 boson. After recalling the non-covariant formalism for decay amplitudes, we derive the expression of the differential decay width and of the polarizations of the final spinning particles, both on- and off-shell. We find an intriguing geometrical interpretation of the results about the polarization. We also illustrate some methods for measuring the polarizations of the resonances and for optimizing data analysis. Then we propose applications to semi-leptonic weak decays, with a major attention to the T-odd component of the polarization; this may help to find, simultaneously, possible time-reversal violations and hints to physics beyond the standard model. We suggest also a CPT test. Last, we discuss some T-odd observables for the production process of f_1 and for the study of the strong final state interactions of non-leptonic decays.

Covariant vacuum polarizations on de Sitter background

We derive covariant expressions for the one-loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter-invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter-invariant formulation does not seem useful, even when it is possible. Our work has two important physical consequences: (1) an upcoming computation of the vacuum polarization from inflationary gravitons should be expressed using the old, noncovariant formalism, and (2) one should re-examine the conclusion of a previous study of the effect of inflationary scalars on gravitons.

Covariant actions for models with nonlinear twisted self-duality

We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the presence of a single auxiliary scalar field. It is shown that the duality-symmetric action should be invariant under the two local symmetries characteristic of this approach, which impose constraints on the form of the action similar to those of Gaillard and Zumino and in the non-covariant formalism. We show that the (twisted) self-duality condition obtained from this action upon integrating its equations of motion can always be recast in a manifestly covariant form which is independent of the auxiliary scalar and thus corresponds to the conventional on-shell duality-symmetric covariant description of the same model. Supersymmetrization of this construction is briefly discussed.

Towards a metamaterial simulation of a spinning cosmic string

The spacetime metric of a spinning cosmic string may be formally represented in flat spacetime by a nonhomogeneous bianisotropic medium. The constitutive parameters of this bianisotropic medium can be established using a noncovariant formalism, thereby paving the way for laboratory simulations of a spinning cosmic string using metamaterial technology.

QUANTUM DETERMINISM FROM QUANTUM GENERAL COVARIANCE

The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder–Weyl formalism. To recover the standard noncovariant formalism without violating covariance, fields need to depend on time in a specific deterministic manner. This deterministic evolution of quantum fields is recognized as a covariant version of the Bohmian hidden-variable interpretation of QFT.

The six-dimensional self-dual tensor

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant form. In particular, it is shown that the field-sttrength tensor satisfies a non-linear generalised self-duality constraint. The self-duality equation is rewritten in five-dimensional notation and shown to be identical to the corresponding equation in the non-covariant formalism.

Remarks on dynamical breaking of chiral symmetry and pion properties in the Nambu and Jona-Lasinio model.

We discuss the mechanism of dynamical breaking of chiral symmetry and pion properties in the Nambu and Jona-Lasinio model. A covariant as well as a noncovariant formalism have been used.Received 31 March 1986DOI:https://doi.org/10.1103/PhysRevD.34.1601©1986 American Physical Society

One-loopN-point functions in the light-cone gauge

We consider, in the light-cone gauge, the possible structure of the counterterms arising in the solution to the renormalization equation. Using the structure of these counterterms and the noncovariant formalism of the integrals as guidelines, we also examine to one-loop order the divergence and nonlocality of theN-point gluon vertex functions forN≧5.

Theory of Relativistic String and Super-Wave Equation. I

In this and succeeding papers we reconstruct the theory of relativistic string, taken as a model of hadrons, in a general and unifying framework. In this paper the classical foundation of the “realistic” string theory is clarified. The theory is derived from the action integral which is invariant under “partial general transformation” on the parameters (σ, τ) for the world sheet traced by a motion of the string, and the fundamental equations are originally covariant under this group. Then by choosing a suitable gauge we obtain Lorentz-covariant formalism associated with constraints. We analyze is characteristics and obtain solutions. Taking another gauge we get the equivalent “Lorentz non-covariant formalism” free from constraint. This directly exhibits the physical meaning of the theory and also leads to its standard Hamiltonian formalism. Several conservation laws characteristic to our string theory are given.