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SUMMARY:Vacuum and 1-particle states in equal-time vs. light-front quantiz
ation
DTSTART;VALUE=DATE-TIME:20180517T203000Z
DTEND;VALUE=DATE-TIME:20180517T205000Z
DTSTAMP;VALUE=DATE-TIME:20211127T175818Z
UID:indico-contribution-3137@indico.jlab.org
DESCRIPTION:Speakers: Jerzy Przeszowski (University of BiaĆystok)\nIn the
canonical quantization procedure the quantum field operators are smeared
with a test function of Schwartz class for coordinates on the quantization
hypersurface\, with a sharp dependence on the temporal parameter. Such qu
antum operators when acting on the vacuum state produce smeared 1-particle
states and higher number particles states. These states\, provided their
norm is finite\, form the Fock space of states.\n\nFor the equal-time quan
tization procedure one needs to diagonalize the Hamiltonian operator\,\nwh
ich can be exactly done mostly only for a free field dynamics. When one im
poses the spectral condition that the spectrum of the Hamiltonian operator
is non-negative for the Fock space states\, then one obtains the definiti
on of the vacuum state and the smeared creation and annihilation operators
. This leads to 1-particle states\, with a sharp dependence on time parame
ter\, which have a finite\, mass dependent norm\, so they belong to the Fo
ck space.\n\nFor the light-front quantization procedure the conditions tha
t the LF Hamiltonian P^{-} and the longitudinal translation kinematic gene
rator P^{+} have non-negative spectra lead only a restriction on the longi
tudinal momentum variable k^{+} > 0. Thus the 1-particle states appear wit
h no dependence on mass but with an infinite norm\, so they do not belong
to the Fock space. However one may evolve these 1-particle states in the l
ight front time by means of the unitary operator and then smear the light
front time dependence with a test function. This extra smearing produces 1
-particle states with a finite norm\, which therefore belong to the Fock s
pace of states. Evidently these final states have mass dependence\, from t
he temporal evolution with the Hamiltonian operator\, but the vacuum state
remains simple with no reference to the Hamiltonian.\n\nAccordingly the 1
-particle states are drastically different within the equal time and the l
ight front formulations\, though they lead to the same physical results. F
or the interacting models\, where the Hamiltonian operator changes number
of particles\, one cannot diagonalize it in the basis of Fock states witho
ut introducing some truncation. Thus the equal time approach is bound to b
e a perturbative formulation. On the contrary the light front procedure gi
ves exact basis for 1-particle states\, which then needs to be evolved in
light front time - where the perturbation calculation enters. Again the li
ght front vacuum state remains simple.\n\nhttps://indico.jlab.org/event/25
2/contributions/3137/
LOCATION:Jefferson Lab - CEBAF Center F113
URL:https://indico.jlab.org/event/252/contributions/3137/
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