scholarly journals Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
A. Tripathi ◽  
B. Chauhan ◽  
A. K. Rao ◽  
R. P. Malik
Keyword(s):  
Brst Quantization ◽  
Relativistic Particle ◽  
Brst Symmetry ◽  
Target Space ◽  
Spinning Particle ◽  
1D Model ◽  
Symmetry Transformations ◽  
The Absolute ◽  
The One ◽  
Relativistic Particles

We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one 0 + 1 -dimensional (1D) model of a free massive spinning relativistic particle (i.e., a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari- (CF-) type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e., a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e., 1D diffeomorphism) invariant models of the (non-)relativistic particles.

scholarly journals QUANTIZATION OF POINTLIKE PARTICLES AND CONSISTENT RELATIVISTIC QUANTUM MECHANICS

2000 ◽  
Vol 15 (28) ◽  
pp. 4499-4538 ◽  
Author(s):  
S. P. GAVRILOV ◽  
D. M. GITMAN
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Positive Spectrum ◽  
The One ◽  
Relativistic Particles

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of the Hilbert space. It allows one not only to include arbitrary backgrounds in the consideration but to get in the course of the quantization consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of the corresponding quantum field. In particular, in a physical sector of the Hilbert space, a complete positive spectrum of energies of relativistic particles and antiparticles is reproduced, and all state vectors have only positive norms.

scholarly journals ABSOLUTE ANTICOMMUTATIVITY OF THE NILPOTENT SYMMETRIES IN THE HAMILTONIAN FORMALISM: FREE ABELIAN 2-FORM GAUGE THEORY

2009 ◽  
Vol 24 (32) ◽  
pp. 6157-6176 ◽  
Author(s):  
R. P. MALIK ◽  
B. P. MANDAL ◽  
S. K. RAI
Keyword(s):  
Gauge Theory ◽  
Time Evolution ◽  
Linear Independence ◽  
Brst Symmetry ◽  
Hamiltonian Formulation ◽  
Hamiltonian Formalism ◽  
Lagrangian Description ◽  
Logical Reason ◽  
Symmetry Transformations ◽  
The Absolute

The celebrated Curci–Ferrari (CF) type of restrictions are invoked to obtain the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations in the context of the Lagrangian description of the physical four (3+1)-dimensional (4D) free Abelian 2-form gauge theory. We show that the above CF-type conditions, which turn out to be the secondary constraints of the theory, remain invariant with respect to the time-evolution of the above 2-form gauge system in the Hamiltonian formulation. This time-evolution invariance (i) physically ensures the linear independence of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry transformations, and (ii) provides a logical reason behind the imposition of the above CF-type restrictions in the proof of the absolute anticommutativity of the off-shell nilpotent (anti-)BRST as well as (anti-)co-BRST symmetry transformations.

scholarly journals Universal Superspace Unitary Operator and Nilpotent (Anti-)Dual-BRST Symmetries: Superfield Formalism

2016 ◽  
Vol 2016 ◽  
pp. 1-17
Author(s):  
T. Bhanja ◽  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Unitary Operator ◽  
Group Structure ◽  
Brst Symmetry ◽  
Rigid Rotor ◽  
Unitary Operators ◽  
Bosonic Field ◽  
Hermitian Conjugate ◽  
Symmetry Transformations ◽  
The One

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP)dualunitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of theAbelian1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show theuniversalityof the SUSPdualunitary operator and its Hermitian conjugate in the cases ofallthe Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of thedualunitary operators and corresponding (anti-)dual-BRST symmetries are completelynovelresults in our present investigation.

scholarly journals Supervariable and BRST Approaches to a Reparameterization Invariant Nonrelativistic System

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
A. K. Rao ◽  
A. Tripathi ◽  
R. P. Malik
Keyword(s):  
Free Particle ◽  
Brst Symmetry ◽  
Symmetry Transformation ◽  
Present System ◽  
Evolution Parameter ◽  
Gauge Fixing ◽  
Symmetry Transformations ◽  
Diffeomorphism Symmetry ◽  
Popov Ghost ◽  
Relativistic Particles

We exploit the theoretical strength of the supervariable and Becchi-Rouet-Stora-Tyutin (BRST) formalisms to derive the proper (i.e., off-shell nilpotent and absolutely anticommuting) (anti-)BRST symmetry transformations for the reparameterization invariant model of a nonrelativistic (NR) free particle whose space x and time t variables are a function of an evolution parameter τ . The infinitesimal reparameterization (i.e., 1D diffeomorphism) symmetry transformation of our theory is defined w.r.t. this evolution parameter τ . We apply the modified Bonora-Tonin (BT) supervariable approach (MBTSA) as well as the (anti)chiral supervariable approach (ACSA) to BRST formalism to discuss various aspects of our present system. For this purpose, our 1D ordinary theory (parameterized by τ ) is generalized onto a 1 , 2 -dimensional supermanifold which is characterized by the superspace coordinates Z M = τ , θ , θ ¯ where a pair of the Grassmannian variables satisfy the fermionic relationships: θ 2 = θ ¯ 2 = 0 , θ   θ ¯ + θ ¯   θ = 0 , and τ is the bosonic evolution parameter. In the context of ACSA, we take into account only the 1 , 1 -dimensional (anti)chiral super submanifolds of the general 1 , 2 -dimensional supermanifold. The derivation of the universal Curci-Ferrari- (CF-) type restriction, from various underlying theoretical methods, is a novel observation in our present endeavor. Furthermore, we note that the form of the gauge-fixing and Faddeev-Popov ghost terms for our NR and non-SUSY system is exactly the same as that of the reparameterization invariant SUSY (i.e., spinning) and non-SUSY (i.e., scalar) relativistic particles. This is a novel observation, too.

scholarly journals Massive Spinning Relativistic Particle: Revisited under BRST and Supervariable Approaches

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
A. Tripathi ◽  
B. Chauhan ◽  
A. K. Rao ◽  
R. P. Malik
Keyword(s):  
Relativistic Particle ◽  
The Novel ◽  
Ordinary Space ◽  
The Absolute ◽  
The One

We discuss the continuous and infinitesimal gauge, supergauge, reparameterization, nilpotent Becchi-Rouet-Stora-Tyutin (BRST), and anti-BRST symmetries and derive corresponding nilpotent charges for the one 0+1-dimensional (1D) massive model of a spinning relativistic particle. We exploit the theoretical potential and power of the BRST and supervariable approaches to derive the (anti-)BRST symmetries and coupled (but equivalent) Lagrangians for this system. In particular, we capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST charges within the framework of the newly proposed (anti-)chiral supervariable approach (ACSA) to BRST formalism where only the (anti-)chiral supervariables (and their suitable super expansions) are taken into account along the Grassmannian direction(s). One of the novel observations of our present investigation is the derivation of the Curci-Ferrari- (CF-) type restriction by the requirement of the absolute anticommutativity of the (anti-)BRST charges in the ordinary space. We obtain the same restriction within the framework of ACSA to BRST formalism by (i) the symmetry invariance of the coupled Lagrangians and (ii) the proof of the absolute anticommutativity of the conserved and nilpotent (anti-)BRST charges. The observation of the anticommutativity property of the (anti-)BRST charges is a novel result in view of the fact that we have taken into account only the (anti-)chiral super expansions.

scholarly journals NILPOTENT SYMMETRIES FOR A FREE RELATIVISTIC PARTICLE IN AUGMENTED SUPERFIELD FORMALISM

2005 ◽  
Vol 20 (23) ◽  
pp. 1767-1779 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Relativistic Particle ◽  
World Line ◽  
Free Particle ◽  
Brst Symmetry ◽  
Dimensional System ◽  
Gravitational Theories ◽  
Target Manifold ◽  
Free Scalar ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the framework of the augmented superfield formalism, the local, covariant, continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry transformations are derived for a (0+1)-dimensional free scalar relativistic particle that provides a prototype physical example for the more general reparametrization invariant string- and gravitational theories. The trajectory (i.e. the world-line) of the free particle, parametrized by a monotonically increasing evolution parameter τ, is embedded in a D-dimensional flat Minkowski target manifold. This one-dimensional system is considered on a (1+2)-dimensional supermanifold parametrized by an even element τ and a couple of odd elements (θ and [Formula: see text]) of a Grassmannian algebra. The horizontality condition and the invariance of the conserved (super)charges on the (super)manifolds play very crucial roles in the above derivations of the nilpotent symmetries. The geometrical interpretations for the nilpotent (anti-)BRST charges are provided in the framework of augmented superfield approach.

scholarly journals (Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
N. Srinivas ◽  
T. Bhanja ◽  
R. P. Malik
Keyword(s):  
Field Theory ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Bosonic Field ◽  
Symmetry Transformations ◽  
The Absolute ◽  
Chiral Superfield ◽  
Chiral Superfields

We exploit the beauty and strength of the symmetry invariant restrictions on the (anti)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations in the case of a two (1+1)-dimensional (2D) self-dual chiral bosonic field theory within the framework of augmented (anti)chiral superfield formalism. Our 2D ordinary theory is generalized onto a (2,2)-dimensional supermanifold which is parameterized by the superspace variable ZM=xμ,θ,θ¯, where xμ (with μ=0,1) are the ordinary 2D bosonic coordinates and (θ,θ¯) are a pair of Grassmannian variables with their standard relationships: θ2=θ¯2=0, θθ¯+θ¯θ=0. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti)chiral superfields (defined on the (anti)chiral (2,1)-dimensional supersubmanifolds of the above general (2,2)-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity, and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti)chiral superfields in our present endeavor.

scholarly journals Description of a new barometer, recently fixed up in the apart­ments of the Royal Society; with remarks on the mode hitherto pursued at various periods, and an account of that which is now adopted, for correcting the observed height of the mercury in the society’s barometer

1843 ◽  
Vol 4 ◽  
pp. 1-3
Keyword(s):  
Royal Society ◽  
The Other ◽  
Chemical Effect ◽  
The Absolute ◽  
The One ◽  
And Control ◽  
Usual Scale

The barometer, here alluded to, may in some measure be consi­dered as two separate and independent barometers, inasmuch as it is formed of two distinct tubes dipping into one and the same cistern of mercury. One of these tubes is made of flint glass, and the other of crown glass, with a view to ascertain whether, at the end of any given period, the one may have had any greater chemical effect on the mercury than the other, and thus affected the results. A brass rod, to which the scale is attached, passes through the framework, between the two tubes, and is thus common to both : one end of which is furnished with a fine agate point, which, by means of a rack and pinion moving the whole rod, may be brought just to touch the surface of the mercury in the cistern, the slightest contact with which is immediately discernible; and the other end of which bears the usual scale of inches, tenths, &c.; and there is a separate vernier for each tube. A small thermometer, the bulb of which dips into the mercury in the cistern, is inserted at the bottom : and an eye­piece is also there fixed, so that the agate point can be viewed with more distinctness and accuracy. The whole instrument is made to turn round in azimuth, in order to verify the perpendicularity of the tubes and the scale. It is evident that there are many advantages attending this mode of construction, which are not to be found in the barometers as usu­ally formed for general use in this country. The absolute heights are more correctly and more satisfactorily determined ; and the per­manency of true action is more effectually noticed and secured. For, every part is under the inspection and control of the observer; and any derangement or imperfection in either of the tubes is imme­diately detected on comparison with the other. And, considering the care that has been taken in filling the tubes, and setting off the scale, it may justly be considered as a standard barometer . The pre­sent volume of the Philosophical Transactions will contain the first register of the observations that have been made with this instru­ment.

scholarly journals Proper BRST quantization of relativistic particles

1994 ◽  
Vol 418 (1-2) ◽  
pp. 353-378 ◽  
Author(s):  
Robert Marnelius
Keyword(s):  
Brst Quantization ◽  
Relativistic Particles

scholarly journals SUPERFIELD FORMULATION OF THE LAGRANGIAN BRST QUANTIZATION METHOD

1995 ◽  
Vol 10 (35) ◽  
pp. 2687-2694 ◽  
Author(s):  
P.M. LAVROV ◽  
P.YU. MOSHIN ◽  
A.A. RESHETNYAK
Keyword(s):  
Gauge Theories ◽  
Brst Quantization ◽  
Brst Symmetry ◽  
Quantization Method ◽  
Ward Identities ◽  
S Matrix ◽  
General Gauge ◽  
Quantization Rules

Lagrangian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the S-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.

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