scholarly journals Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals

2000 ◽  
Vol 78 (8) ◽  
pp. 769-777 ◽  
Author(s):  
A T Suzuki ◽  
A GM Schmidt

The well-known D-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be identified with Grassmannian integration in positive dimensions. From this possibility follows the concept of negative-dimensional integration for loop integrals in field theories. Using this technique, we evaluate three two-loop three-point scalar integrals, with five and six massless propagators, with specific external kinematic configurations (two legs on-shell), and four three-loop two-point scalar integrals. These results are given for arbitrary exponents of propagators and dimension, in Euclidean space, and the particular cases compared to results published in the literature. PACS Nos.: 02.90+p, 11.15Bt, 12.38Bx

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Marco Bochicchio ◽  
Mauro Papinutto ◽  
Francesco Scardino

Abstract We compute, to the lowest perturbative order in SU(N) Yang-Mills theory, n-point correlators in the coordinate and momentum representation of the gauge-invariant twist-2 operators with maximal spin along the p+ direction, both in Minkowskian and — by analytic continuation — Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.


Author(s):  
Jae-Kwang Hwang

Space-time evolution is briefly explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (E=cDtDV), charges (|q|= cDt) and absolute time (ct) are newly defined based on the 4-D Euclidean space. The big bang is understood by the space-time evolution of the 4-D Euclidean space but not by the sudden 4-D Minkowski space-time creation. The big bang process created the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry. Our universe is the matter universe with the negative charges of electric charge (EC), lepton charge (LC) and color charge (CC). This first universe is made of three dark matter -, lepton -, and quark - primary black holes with the huge negative charges which cause the Coulomb repulsive forces much bigger than the gravitational forces. The huge Coulomb forces induce the inflation of the primary black holes, that decay to the super-massive black holes. The dark matter super-massive black holes surrounded by the normal matters and dark matters make the galaxies and galaxy clusters. The spiral arms of galaxies are closely related to the decay of the 3-D charged normal matter black holes to the 1-D charged normal matter black holes. The elementary leptons and quarks are created by the decay of the normal matter charged black holes, that is caused by the Coulomb forces much stronger than the gravitational forces. The Coulomb forces are very weak with the very small Coulomb constants (k1(EC) = kdd(EC) ) for the dark matters and very strong with the very big Coulomb constants (k2(EC) = knn(EC)) for the normal matters because of the non-communication of the photons between the dark matters and normal matters. The photons are charge dependent and mass independent. But the dark matters and normal matters have the similar and very weak gravitational forces because of the communication of the gravitons between the dark matters and normal matters. The gravitons are charge independent and mass dependent. Note that the three kinds of charges (EC, LC and CC) and one kind of mass (m) exist in our matter universe. The dark matters, leptons and quarks have the charge configurations of (EC), (EC,LC) and (EC,LC,CC), respectively. Partial masses of elementary fermions are calculated, and the proton spin crisis is explained. The charged black holes are not the singularities.


2004 ◽  
Vol 19 (22) ◽  
pp. 3637-3667 ◽  
Author(s):  
KATRIN WENDLAND

We consider orbifolds of two-dimensional unitary toroidal superconformal field theories with target spaces of arbitrary dimensions, where the orbifold group involves the space–time fermion number operator. We construct all so-called superaffine, orbifold prime and super-M-orbifold models by generalizing the constructions of Dixon, Ginsparg and Harvey. We also correct claims made by Dixon, Ginsparg and Harvey about multicritical points among those models with central charge [Formula: see text].


1968 ◽  
Vol 64 (4) ◽  
pp. 1071-1079 ◽  
Author(s):  
J. V. Narlikar

AbstractIt is well known that classical electrodynamics can be described both as a field theory and as a theory of direct interparticle action. In the present paper it is shown that, provided certain general conditions are satisfied, fields of arbitrary spin have their counterparts in ‘direct particle fields’. This correspondence between the two formalisms is established in the Riemannian space-time used for general relativity.


2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.


1991 ◽  
Vol 06 (31) ◽  
pp. 2843-2854 ◽  
Author(s):  
AMIT GIVEON

Target space duality symmetry of the SL (2,ℝ)/ U (1) background leads to stringy properties of the black hole. For a Euclidean space-time the semi-infinite cigar is transformed to an infinite funnel. High and low temperatures of the black hole are related. For a Lorentzian space-time, duality interchanges regions I and V in the Kruskal–Szekeres coordinates, that is, duality exchanges the horizon with the singularity. As a result, a signal can be sent out of the singularity. Such a signal is associated with the string winding modes. The mass of the black hole and the consequence of a tachyon disturbance are discussed.


2003 ◽  
Vol 18 (33n35) ◽  
pp. 2525-2532 ◽  
Author(s):  
ALESSANDRO TORRIELLI

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.


2017 ◽  
Vol 32 (28n29) ◽  
pp. 1730021 ◽  
Author(s):  
Corinne de Lacroix ◽  
Harold Erbin ◽  
Sitender Pratap Kashyap ◽  
Ashoke Sen ◽  
Mritunjay Verma

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 noncompact space–time dimensions, but suffers from the usual infrared divergences when the number of noncompact space–time dimensions is 4 or less.


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