The Wightman Formalism

Bogolubov, N. N.; Логунов, А. А.; Oksak, A. I.; Todorov, Ivan; Gould, G. G.

doi:10.1007/978-94-009-0491-0_8

Cited by 16 publications

(19 citation statements)

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“…It turns out that, in case the field φ is massless, the above quantization procedure is the only consistent one (in d=1+1), if one wants to use light-like hypersurfaces (Bogolubov et al 1990). However, it is important to note that the characteristic initial-value problem does not correspond to light-cone quantization.…”

Section: Quantization As An Initial-and/or Boundary-value Problemmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

114

141

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Abstract. These lecture notes review the foundations and some applications of lightcone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincaré invariance naturally leads to Dirac's forms of relativistic dynamics. Among these, the front form, being the basis for light-cone quantization, is my main focus. I explain a few of its peculiar features such as boost and Galilei invariance or separation of relative and center-of-mass motion. Combining light-cone dynamics and field quantization results in light-cone quantum field theory. As the latter represents a first-order system, quantization is somewhat nonstandard. I address this issue using Schwinger's quantum action principle, the method of Faddeev and Jackiw, and the functional Schrödinger picture. A finite-volume formulation, discretized light-cone quantization, is analysed in detail. I point out some problems with causality, which are absent in infinite volume. Finally, the triviality of the light-cone vacuum is established. Coming to applications, I introduce the notion of light-cone wave functions as the solutions of the light-cone Schrödinger equation. I discuss some examples, among them nonrelativistic Coulomb systems and model field theories in two dimensions. Vacuum properties (like chiral condensates) are reconstructed from the particle spectrum obtained by solving the light-cone Schrödinger equation. In a last application, I make contact with phenomenology by calculating the pion wave function within the Nambu and Jona-Lasinio model. I am thus able to predict a number of observables like the pion charge and core radius, the r.m.s. transverse momentum, the pion structure function and the pion distribution amplitude. The latter turns out to be the asymptotic one.

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Section: Quantization As An Initial-and/or Boundary-value Problemmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

114

141

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“…Classical energy density is always positive, which is to say that the stress-energy tensor for a scalar field satisfies the weak energy condition (WEC) T µν u µ u ν ≥ 0, where u µ is a causal vector. In quantum field theory [1,2] it is impossible. There are states |Υ that violate WEC, namely Υ|T µν u µ u ν |Υ ≤ 0 holds [47], where T µν now is a renormalized stress energy operator.…”

Section: Discussionmentioning

confidence: 99%

“…Localized detection events provide the experimental basis of quantum field theory and quantum optics [1][2][3]. They are critical for understanding relativistic aspects of quantum information processing [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Localization of relativistic particles and uncertainty relations

Terno

2014

Phys. Rev. A

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Localization of relativistic particles and their position-momentum uncertainty relations are not yet fully understood. We discuss two schemes of photon localization that are based on the energy density. One scheme produces a positive operator-valued measure for localization. It coincides with the number density operator and reproduces an effective 3 × 3 polarization density matrix. Another scheme results in a probability distribution that is conditioned on the detection. In both schemes the uncertainty relations for transversal position and momentum approach the Heisenberg bound ∆p∆z = 1 2 .

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“…According to Wigner's theorem [24] given a bijection P 1 (H) → P 1 (H) (P → P ′ ) which preserves transition probabilities, there exists a unitary or antiunitary operator U on H such that…”

Section: B Symmetries In Traditional Quantum Mechanics In the Hpo Fomentioning

confidence: 99%

Symmetries and Conservation Laws in Histories-Based Theories

Dass¹,

Joglekar²

2001

Annals of Physics

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Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of 'temporal sequences' of 'events' using partial semigroups) and logic structure for 'single-time histories'. Symmetries are classified into orthochronous (those preserving the 'temporal order' of 'events') and nonorthochronous. A straightforward criterion for physical equivalence of histories is formulated in terms of orthochronous symmetries; this criterion covers various notions of physical equivalence of histories considered by Gell-Mann and Hartle as special cases. In familiar situations, a reciprocal relationship between traditional symmetries (Wigner symmetries in quantum mechanics and Borel-measurable transformations of phase space in classical mechanics) and symmetries defined in this work is established. In a restricted class of theories, a definition of conservation law is given in the history language which agrees with the standard ones in familiar situations; in a smaller subclass of theories, a Noether type theorem (implying a connection between continuous symmetries of dynamics and conservation laws) is proved. The

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The Wightman Formalism

Cited by 16 publications

References 0 publications

Light-Cone Quantization: Foundations and Applications

Light-Cone Quantization: Foundations and Applications

Localization of relativistic particles and uncertainty relations

Symmetries and Conservation Laws in Histories-Based Theories

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