<i>An Introduction to Quantum Field Theory</i>

Peskin, Michael E.; Schroeder, Daniel V.; Martinec, Emil J.

doi:10.1063/1.2807734

Cited by 956 publications

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“…In coordinate space, the Fourier transform of this function is the Feynman propagator D F (x), which has non-zero support inside and outside the light cone (for example, see section 2.4 of [7]). However, with a different i prescription, the Fourier transform of 1/P 2 in four dimensions has its support on the light cone.…”

Section: Jhep10(2004)074mentioning

confidence: 99%

Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory

Cachazo¹,

Svrcek²,

Witten³

2004

J. High Energy Phys.

143

204

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Section: Jhep10(2004)074mentioning

confidence: 99%

Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory

Cachazo¹,

Svrcek²,

Witten³

2004

J. High Energy Phys.

143

204

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“…Cartan's and Bain's preference for unification, which they thought unsatisfiable, is adequately realized using OP spinors, for which the group that makes ψ a spinor is the (double cover of) a Lorentz group that is a subgroup of the space-time coordinate transformations. OP spinors, unlike the spinors of the tetrad formalism, are thus a strict generalization of the spinors in Minkowski space-time in Cartesian coordinates, such as one finds in standard particle physics books [Kaku, 1993, Peskin andSchroeder, 1995]. While the answers regarding spinors and the conventionality of simultaneity have varied considerably, and all the previous answers have flaws, the question is a very welcome one in the sense that it provides a rare instance of consideration of the relevance of electrons, protons, and the like to philosophical questions about space-time theory.…”

Section: Spinors and The Partial Conventionality Of Simultaneitymentioning

confidence: 99%

The nontriviality of trivial general covariance: How electrons restrict ‘time’ coordinates, spinors (almost) fit into tensor calculus, and of a tetrad is surplus structure

Pitts

2012

Studies in History and Philosophy of Science Part B: Studies in

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It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus.On the other hand, the physics literature often claims that spinors as such cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is (nearly) Ockhamized, with most of the fluff removed. As developed * Forthcoming in Studies in History and Philosophy of Modern Physics 1 nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix diag(−1, 1, 1, 1), the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and values of the fields involved.Apart from coordinate order and the usual spinorial two-valuedness, (densitized) Ogievetsky-Polubarinov spinors form, with the (conformal part of the) met- The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited.

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“…1 yields the two terms A (2) 11 + 2A (2) 21 , where the first will be linear in the couplings coming from L (1) , and the latter will depend only on L (0) .…”

Section: Rge For the Highest Polesmentioning

confidence: 99%

“…A ( The meaning of these equations is as follows: the first one implies that the part of the subleading poles that comes from two-loop diagrams is given by the single pole from one-loop diagrams (A (3) 11 ) after one has substituted one L (1) (L (2) ) vertex with A (1) 11 (A (2) 11 ). According to the second one the double pole coming from three-loop diagrams is given by two terms: the first one is obtained from single poles from two-loop diagrams after substitution of one L (1) vertex with A (1) 11 , and the second one from single poles from one-loop diagrams after substitution of one L (2) vertex with 2A (2) 21 , i.e.…”

Section: Rge For the Subleading Polesmentioning

confidence: 99%

“…According to the second one the double pole coming from three-loop diagrams is given by two terms: the first one is obtained from single poles from two-loop diagrams after substitution of one L (1) vertex with A (1) 11 , and the second one from single poles from one-loop diagrams after substitution of one L (2) vertex with 2A (2) 21 , i.e. the subleading poles of one -order lower.…”

Section: Rge For the Subleading Polesmentioning

confidence: 99%

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Renormalization group equations

Dittrich¹

Lecture Notes in Physics

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We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral perturbation theory, e.g., this means that one can obtain the series of leading chiral logs by calculating only one loop diagrams. We discuss also the renormalization group equations for the subleading divergences, and the crucial role of counterterms that vanish at the equations of motion. Finally, we show that the renormalization group equations obtained here apply equally well also to renormalizable theories.

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An Introduction to Quantum Field Theory

Cited by 956 publications

References 0 publications

Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory

Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory

The nontriviality of trivial general covariance: How electrons restrict ‘time’ coordinates, spinors (almost) fit into tensor calculus, and of a tetrad is surplus structure

Renormalization group equations

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