Canonical quantization on the light cone

1983 ◽  
Vol 54 (2) ◽  
pp. 141-149
Author(s):  
F. A. Lunev
Keyword(s):  
Light Cone ◽  
Canonical Quantization

scholarly journals Role of zero modes in the canonical quantization of heavy-fermion QED in light-cone coordinates

1993 ◽  
Vol 48 (12) ◽  
pp. 5873-5882 ◽  
Author(s):  
Robert W. Brown ◽  
Jin Woo Jun ◽  
Shmaryu M. Shvartsman ◽  
Cyrus C. Taylor
Keyword(s):  
Light Cone ◽  
Heavy Fermion ◽  
Canonical Quantization ◽  
Zero Modes

CONSISTENCY BETWEEN LIGHT-FRONT QUANTIZATION AND COVARIANTIZATION FOR ZERO MODES

2005 ◽  
Vol 20 (19) ◽  
pp. 1459-1464
Author(s):  
ALFREDO T. SUZUKI ◽  
RICARDO BENTÍN
Keyword(s):  
Light Cone ◽  
Ad Hoc ◽  
Vector Boson ◽  
Canonical Quantization ◽  
Direct Consequence ◽  
Mathematical Treatment ◽  
Abelian Gauge ◽  
Light Cone Gauge ◽  
Treatment Research ◽  
Light Front Quantization

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional "spurious" or "unphysical" pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory.

scholarly journals Light-front and conformal field theories in two dimensions

2018 ◽  
Vol 33 (22) ◽  
pp. 1850119
Author(s):  
Pierre Grangé ◽  
Ernst Werner
Keyword(s):  
Reference Frame ◽  
Light Cone ◽  
Mathematical Formulation ◽  
Canonical Quantization ◽  
Two Dimensions ◽  
Light Front ◽  
Classical Solutions ◽  
Necessary Condition ◽  
Test Function ◽  
Conformal Field

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables [Formula: see text], [Formula: see text] pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth [Formula: see text] fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the [Formula: see text] and [Formula: see text] expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation.

Light-cone QCD on the lattice

2000 ◽  
Vol 83-84 (1-3) ◽  
pp. 116-120 ◽  
Author(s):  
S Dalley
Keyword(s):  
Light Cone

scholarly journals Light-cone sum rules for proton decay

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ulrich Haisch ◽  
Amando Hala
Keyword(s):  
Lattice Qcd ◽  
Light Cone ◽  
Sum Rules ◽  
State Of The Art ◽  
Form Factors ◽  
Baryon Number ◽  
Proton Decay ◽  
Matrix Elements ◽  
Decay Channels ◽  
Systematic Uncertainties

Abstract We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

Masslessness and light-cone propagation in 3+2 de Sitter and 2+1 Minkowski spaces

1986 ◽  
Vol 33 (2) ◽  
pp. 415-420 ◽  
Author(s):  
M. Flato ◽  
C. Fronsdal ◽  
J. P. Gazeau
Keyword(s):  
Light Cone ◽  
De Sitter ◽  
Minkowski Spaces
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