A massive non-abelian vector model

Recently, interest has been focused on quantum field theories in which a Lagrange multiplier field occurs in the classical Lagrangian. This has the effect of restricting the sum over classical paths in the path integral to solutions of the classical field equation. Examples of such theories are the dynamical theory of two-dimensional gravity proposed by Jackiw and Teitelboim, the Chern–Simons formulation of gravity in 2 + 1 dimensions by Witten, and the path-integral formulation of classical systems by Gozzi. We examine, in this paper, a gauge theory in which a vector field [Formula: see text] acts as a Lagrange multiplier in the classical Lagrangian, ensuring that a vector field [Formula: see text] satisfies the Yang–Mills equations of motion. Quantization can be carried out either using BRST quantization or by using the Faddeev–Popov procedure. Either by explicitly integrating over the field [Formula: see text] and its associated ghost fields, or by directly examining the Feynman perturbation theory, it can be established that all diagrams beyond one-loop order vanish, allowing one to compute the one-particle irreducible generating functional exactly. Background-field quantization is introduced to simplify the renormalization program. The β function is computed in closed form. In an appendix we show how our interaction can be derived from Yang–Mills theory based on a group G or by considering the Yang–Mills theory for a group IG. This can be extended to deal with four interacting gauge fields. A second appendix deals with a scalar model that superficially resembles our vector model.

Download Full-text

Thermal Gauge Theories with Lagrange Multiplier Fields

Canadian Journal of Physics ◽

10.1139/cjp-2021-0248 ◽

2021 ◽

Author(s):

F.T. Brandt ◽

J. Frenkel ◽

S. Martins-Filho ◽

G.S.S Sakoda ◽

D.G.C. McKeon

Keyword(s):

Quantum Gravity ◽

Lagrange Multiplier ◽

Finite Temperature ◽

Gauge Theories ◽

Equations Of Motion ◽

Path Integrals ◽

Radiative Corrections ◽

Loop Order ◽

Yang Mills

We study the Yang-Mills theory and quantum gravity at finite temperature, in the presence of La-grange multiplier fields. These restrict the path integrals to field configurations which obey the classical equations of motion. This has the effect of doubling the usual one–loop thermal contributions and of suppressing all radiative corrections at higher loop order. Such theories are renormalizable at all temperatures. Some consequences of this result in quantum gravity are briefly examined.

Download Full-text

Electron Trajectories in Molecular Orbitals

10.26434/chemrxiv.12047376 ◽

2020 ◽

Author(s):

Isaiah Sumner ◽

Hannah Anthony

Keyword(s):

Lagrange Multiplier ◽

Equations Of Motion ◽

Bohmian Mechanics ◽

Molecular Orbitals ◽

Quantum Hydrodynamics ◽

Relativistic Limit ◽

Quantum Particles ◽

Quantum Force ◽

Trajectory Methods ◽

Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

Download Full-text

Dynamics Simulation of Capsule Filling Machine Based Virtual Prototype

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.127.582 ◽

2011 ◽

Vol 127 ◽

pp. 582-587 ◽

Cited By ~ 1

Author(s):

Gui He Wang ◽

Yong Guo Zhang ◽

Tian Biao Yu ◽

Wan Shan Wang

Keyword(s):

Lagrange Multiplier ◽

Geometric Model ◽

Equations Of Motion ◽

Virtual Prototype ◽

Transmission Mechanism ◽

Lagrange Multiplier Method ◽

Dynamics Simulation ◽

Multiplier Method ◽

Interface Module

Capsule filling machine is the key filling equipment for pharmaceutical capsule preparations. Taking NJP3400 type of capsule filling machine as an example, we analyze its principle and characteristics successfully. First, we built its geometric model with Pro/E software, established the equations of motion of transmission mechanism with Lagrange multiplier method and showed the process of solving the equations with GSTIFF software. With the interface module called mechpro of PRO-ADAMS, the model was imported into ADAMS, and then, we analyze the machine’s strength, displacement, acceleration and the association of these parameters.

Download Full-text

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Advances in Mathematical Physics ◽

10.1155/2017/7397159 ◽

2017 ◽

Vol 2017 ◽

pp. 1-49 ◽

Cited By ~ 17

Author(s):

Alexei A. Deriglazov ◽

Walberto Guzmán Ramírez

Keyword(s):

General Relativity ◽

Relativistic Quantum ◽

Equations Of Motion ◽

Three Dimensional ◽

Theoretical Description ◽

Vector Model ◽

Relativistic Quantum Mechanics ◽

Spinning Particle ◽

Rotating Body ◽

Relativistic Spin

We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

Download Full-text

A NOTE ON THE (ANTI-)BRST INVARIANT LAGRANGIAN DENSITIES FOR THE FREE ABELIAN 2-FORM GAUGE THEORY

Modern Physics Letters A ◽

10.1142/s0217732310033323 ◽

2010 ◽

Vol 25 (28) ◽

pp. 2457-2467

Author(s):

SAURABH GUPTA ◽

R. P. MALIK

Keyword(s):

Gauge Theory ◽

Vector Field ◽

Lagrange Multiplier ◽

Field Condition ◽

Equations Of Motion ◽

Present Theory ◽

Lagrange Equations ◽

Symmetry Transformations ◽

The Absolute ◽

Lagrangian Densities

We show that the previously known off-shell nilpotent [Formula: see text] and absolutely anticommuting (sb sab + sab sb = 0) Becchi–Rouet–Stora–Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci–Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler–Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.

Download Full-text

REVISITING THE MODIFIED STAROBINSKY MODEL WITH A COSMOLOGICAL CONSTANT

International Journal of Modern Physics D ◽

10.1142/s0218271809015138 ◽

2009 ◽

Vol 18 (09) ◽

pp. 1355-1366 ◽

Cited By ~ 1

Author(s):

ANA PELINSON

Keyword(s):

Cosmological Constant ◽

Equations Of Motion ◽

Quantum Effects ◽

Radiative Corrections ◽

Susy Particle ◽

Particle Content ◽

Starobinsky Model ◽

Last Stage ◽

The Masses ◽

Matter Fields

The Starobinsky model is a natural inflationary scenario in which inflation arises due to quantum effects of the massless matter fields. A modified version of the Starobinsky (MSt) model takes the masses of matter fields and the cosmological constant, Λ, into account. The equations of motion become much more complicated; however, approximate analytic and numeric solutions are possible. In the MSt model, inflation starts due to the supersymmetric (SUSY) particle content of the underlying theory, and the transition to the radiation-dominated epoch occurs due to the relatively heavy s-particles decoupling. For Λ = 0 the inflationary solution is stable until the last stage, just before decoupling. In the present paper we generalize this result for Λ ≠ 0, since Λ should be nonvanishing at the SUSY scale. We also take into account the radiative corrections to Λ. The main result is that the inflationary solution of the MSt model remains robust and stable.

Download Full-text

Vector model of the timing diagram of automatic machine

Mechanical Sciences ◽

10.5194/ms-4-391-2013 ◽

2013 ◽

Vol 4 (2) ◽

pp. 391-396 ◽

Cited By ~ 3

Author(s):

A. Jomartov

Keyword(s):

Transfer Functions ◽

Equations Of Motion ◽

Automatic Machine ◽

Vector Model ◽

Timing Diagrams ◽

Timing Diagram

Abstract. In this paper a vector model of timing diagram of automatic machine is developed, which allows us to solve a variety dynamic tasks by changing the parameters of timing diagram of its mechanisms. The connection between the parameters of the timing diagram of automatic machine and equations of motion mechanisms through functions of position and transfer functions of mechanisms is established. The vector model of timing diagram can be used to optimize the timing diagrams of looms and polygraphic machines.

Download Full-text

Dynamics Analysis of a Sinking Winch Mechanism

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.105-107.454 ◽

2011 ◽

Vol 105-107 ◽

pp. 454-457

Author(s):

Xing Guo Shao ◽

Zhen Cai Zhu ◽

Guo Hua Cao ◽

Yi Lei Li

Keyword(s):

Numerical Simulation ◽

Dynamic Analysis ◽

Lagrange Multiplier ◽

Simulation Study ◽

Equations Of Motion ◽

Dynamics Analysis ◽

Unilateral Constraints ◽

Dynamics Model ◽

Midpoint Method ◽

Smooth Dynamics

This paper investigates the dynamics of a sinking winch mechanism in the framework of non-smooth dynamics. The previous works ignored the unilateral property of the cable (it can only pull the platform but can’t push it), which is specially taken into consideration in this paper. We propose the set-valued tension law to model the unilateral constraints of the cables. The equations of motion are derived by use of the Lagrange multiplier method. The dynamics model of the mechanism is obtained by combining the equations of motion and the set-valued tension law. Its solution is solved by the Moreau midpoint method. We present a numerical simulation study to demonstrate that the non-smooth dynamics framework is effective and suitable for the dynamic analysis of the sinking winch mechanism.

Download Full-text

Electron Trajectories in Molecular Orbitals

10.26434/chemrxiv.12047376.v1 ◽

2020 ◽

Author(s):

Isaiah Sumner ◽

Hannah Anthony

Keyword(s):

Lagrange Multiplier ◽

Equations Of Motion ◽

Bohmian Mechanics ◽

Molecular Orbitals ◽

Quantum Hydrodynamics ◽

Relativistic Limit ◽

Quantum Particles ◽

Quantum Force ◽

Trajectory Methods ◽

Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

Download Full-text