PROPAGATOR FOR THE RELATIVISTIC SPINNING PARTICLE VIA FUNCTIONAL INTEGRAL OVER TRAJECTORIES

1988 ◽  
Vol 03 (16) ◽  
pp. 1551-1559 ◽  
Author(s):  
A. YU. ALEKSEEV ◽  
S.L. SHATASHVILI
Keyword(s):  
Path Integral ◽  
Coadjoint Orbit ◽  
Arbitrary Spin ◽  
Functional Integral ◽  
Spinning Particle ◽  
Spin Factor ◽  
Definition Of

A spin factor is defined by means of the canonical 2-form on the coadjoint orbit of the SO (d+1) group. Including this spin factor in the definition of the path integral leads to the correct propagator for a system of arbitrary spin in a space of dimension d.

scholarly journals WORLDSHEET COVARIANT PATH INTEGRAL QUANTIZATION OF STRINGS

2006 ◽  
Vol 21 (32) ◽  
pp. 6525-6574 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Path Integral ◽  
First Principles ◽  
Critical Dimension ◽  
Functional Integral ◽  
Integral Approach ◽  
Vertex Operators ◽  
General Covariance ◽  
Classical Transformation ◽  
Definition Of ◽  
Independent Path

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

scholarly journals Polyakov's spin factor for a classical spinning particle via the BRST invariant path integral

1994 ◽  
Vol 327 (3-4) ◽  
pp. 274-278 ◽  
Author(s):  
Jin-Ho Cho ◽  
Seungjoon Hyun ◽  
Hyuk-jae Lee
Keyword(s):  
Path Integral ◽  
Spinning Particle ◽  
Spin Factor

Path integral for spinning particle in magnetic field via bosonic coherent states

1995 ◽  
Vol 36 (4) ◽  
pp. 1602-1615 ◽  
Author(s):  
T. Boudjedaa ◽  
A. Bounames ◽  
L. Chetouani ◽  
T. F. Hammann ◽  
Kh. Nouicer
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Coherent States ◽  
Spinning Particle

Euclidean path integrals and quantum mechanics (QM)

2021 ◽  
pp. 18-41
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Correlation Functions ◽  
Path Integrals ◽  
Continuous Phase ◽  
Functional Integral ◽  
Smooth Transition ◽  
Path Integral Representation ◽  
The Matrix ◽  
Functional Measure

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.

scholarly journals COORDINATE-INVARIANT PATH INTEGRAL METHODS IN CONFORMAL FIELD THEORY

2006 ◽  
Vol 21 (17) ◽  
pp. 3525-3563 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Direct Calculation ◽  
Conformal Anomaly ◽  
Operator Formalism ◽  
Conformal Field ◽  
Integral Methods ◽  
Change Of Variables ◽  
Definition Of

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals A THEORY OF ALGEBRAIC INTEGRATION

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2293-2297
Author(s):  
R. CASALBUONI
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Path Integral ◽  
Physical Principle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
The One ◽  
Definition Of

In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such spaces. We consider this problem and we show how to define an integration which respects the physical principle of composition of the probability amplitudes for a very large class of algebras.

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