Constrained Field Theories Research Articles

Cosmic web & caustic skeleton: non-linear constrained realizations — 2D case studies

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed non-linear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.

Possible existence of chiral and multiple chiral nuclei in thallium isotopes * *This work is partly support by the Major Program of Natural Science Foundation of Shandong Province (ZR2020ZD30), the Outstanding Youth Fund of Natural Science Foundation of Shandong Province (ZR2020YQ07), the National Natural Science Foundation of China (11675094, 12075138), and the Young Scholars Program of Shandong University, Weihai. The

The chirality in thallium isotopes is investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field theory. Several minima with prominent triaxial deformation and proper configuration, where the chiral doublet bands may appear, are obtained in odd-odd nuclei Tl and odd-mass nuclei Tl. Furthermore, the possible existence of multiple chiral doublet bands (MχD) is demonstrated in Tl. As the chiral doublet bands in Tl and MχD in 195Tl have been observed experimentally, further experimental exploration for the chirality in Tl and MχD in thallium isotopes is expected to verify the predictions.

Possible Candidates for Chirality in the Odd-Odd As IsotopesSupported by the National Natural Science Foundation of China (Grant Nos. 11705102 and 11675094), the Shandong Natural Science Foundation (Grant No. JQ201701), and the Young Scholars Program of Shandong University, Weihai.

The deformations and the corresponding configurations of the odd-odd As isotopes are investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) theory. Energy minima with triaxial deformations and high-j particle-hole configurations are obtained in 72,74,76,78,80As, where the chiral doublet bands are possible to appear. The existence of multiple chiral doublet (MχD) is demonstrated in 74,76,78As. Based on the calculated single-particle levels, we also find possible coexistence of chiral and pseudospin symmetries in the odd-odd As isotopes.

A Novel Covariant Approach to Gravito-Electromagnetism

This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter field. Equations of motion, continuity equation, energy conservation, field tensor, energy-momentum tensor, constraints and Lagrangian formulation are presented as a simple and unified formulation that can be useful for future research.

Constrained field theories on Kerr backgrounds

We analyze the constraints of gauge theories on Kerr and Kerr-de Sitter spacetimes, which contain one or more horizons. We find that the constraints are modified on such backgrounds through the presence of additional surface terms at the horizons. As a concrete example, we consider the Maxwell field and find that the Gauss law constraint involves surface corrections at the horizons. These surface contributions correspond to induced surface charges and currents on the horizons, which agree with those found within the membrane paradigm. The modification of the Gauss law constraint also influences the gauge fixing and Dirac brackets of the theory.

Constrained field theories on spherically symmetric spacetimes with horizons

We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.

Note on scalars, perfect fluids, constrained field theories, and all that

The relation of a scalar field with a perfect fluid has generated some debate along the last few years. In this Letter we argue that shift-invariant scalar fields can describe accurately the potential flow of an isentropic perfect fluid, but, in general, the identification is possible only for a finite period of time. After that period in the evolution the dynamics of the scalar field and the perfect fluid branch off. The Lagrangian density for the velocity-potential can be read directly from the expression relating the pressure with the Taub charge and the entropy per particle in the fluid, whereas the other quantities of interest can be obtained from the thermodynamic relations.

Constrained variational calculus for higher order classical field theories

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner–Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Chetaev versus vakonomic prescriptions in constrained field theories with parametrized variational calculus

Starting from a characterization of admissible Chetaev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the nonholonomic field equations. We present an example in field theory where the nonholonomic method proved to be unphysical.

EQUIVALENCE BETWEEN DIFFERENT CLASSICAL TREATMENTS OF THE O(N) NONLINEAR SIGMA MODEL AND THEIR FUNCTIONAL SCHRÖDINGER EQUATIONS

In this work we derive the Hamiltonian formalism of the O(N) nonlinear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrödinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrödinger representation.

Low-Energy Theorems in the Chiral Soliton Model

We show that low-energy theorems for pion-photoproduction and Compton scattering can be reproduced within the Skyrme-soliton model using the formulation developed for pion­ nucleon scattering. The electric polarizability of nucleon is shown to be given by a disper­ sion integral with the longitudinal-photon absorption cross section, while the magnetic one is given by using the dispersion integral. We explicitly give contributions from the L1 state as the resonance and the 1rL1 channel coupling. We have recently shown that the soft-pion theorems such as the Goldberger­ Treiman, Adler-Weisberger and Tomozawa-Weinberg relations, can be reproduced within the Skyrme-soliton model. 1' In this treatment, we developed a full-field method for the soliton model. The method gives the same amplitudes as those of the usual collective coordinate method using a constrained field theory. In the method, the same Born amplitude can be obtained by assuming the full field to be an interpolat­ ing field between the asymptotic in and out fields. Here, we do not decompose the field into the soliton and the fluctuating fields. This method is superior to the former one, because the axial-vector and vector currents are found to satisfy the current algebra. The soft-pion theorems can be straightforwardly proven such as the Adler-Weisberger (AW) and the Tomozawa-Weinberg (TW) relations. Whether low-energy theorems (LET) are reproduced is a crucial test both for models of nucleon and for approximations, because LET are based on general principles such as current algebra, partially conserving axial-vector current and gauge invariance. We tried in a previous paper 2 ' to reproduce the LET for pion­ photoproduction3' in the model: We have shown that the LET is reproduced for leading order in mn:/M through the electric and magnetic Born terms, but not com­ pletely for terms linear in mn:/M, where M(mn:) is the nucleon (pion) mass. In this work we try to reproduce this linear term following the method of Low,4' and then investigate the Compton scattering involving the electromagnetic polar­ izabilities of the nucleon. § 2. Full field method in the Skyrme model In the usual approach to the pion-nucleon scattering in the Skyrme model we

Constrained topological field theory

We derive a model of constrained topological gravity, a theory recently introduced by us through the twist of N = 2 Liouville theory, starting from the general BRST algebra and imposing the moduli space constraint as a gauge fixing. To do this, it is necessary to introduce a formalism that allows a careful treatment of the global and the local degrees of freedom of the fields. Surprisingly, the moduli space constraint arises from the simplest and most natural gauge-fermion ( antighost x Lagrange multiplier), confirming the previous results. The simplified technical set-up provides a deeper understanding for constrained topological gravity and a convenient framework for future investigations, like the matter coupling and the analysis of the effects of the constraint on the holomorphic anomaly.

Functional integration method for the Hubbard model with large negativeU and other local pairing models

We formulate a constrained field theory as a representation of the Hubbard model with strong attractive (‘negativeU’) coupling. The superconducting mean-field solutions are correctly reproduced after unusual antiperiodicity conditions on grassmann fields were imposed. In the exact action we find a new doubly-local symmetry, which together with Elitzur's theorem predicts strong corrections to mean field approximations by quantum fluctuations. We compare results for the large negativeU Hubbard model with those for other local pairing models, including disorder too. A new subclassification scheme of type II superconductivity is proposed. For disordered models, we discuss implications of Elitzur's theorem for the existence of superconducting glass phases.

Jordan algebra field theory

It is shown that the set of observable functionals associated with a constrained field theory satisfying two given assumptions is a Jordan algebra under the symmetric Dirac bracket composition law.