I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is to...

This is an account of some recent work done with H. S. La [1] [2], based ultimately on the work of Fischler and Susskind [3] and Polchinski [4]. Disciplines Physical Sciences and Mathematics | Physics This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/548 Beyond Conformal Field Theory

We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.

(a) If p ramifies in Q(ζm), then p | m; the ramification index ep of the primes over p is φ(p) = (p− 1)pk−1 if p ‖ m. (b) The prime p is wildly ramified in Q(ζm) if and only if p | m. (c) If p m, then p is unramified. In the ring of integers Z[ζm] of Q(ζm), we obtain pOL = ∏gp i=1 pi. The primes pi have residue class degree fp = [Fp(ζm) : Fp], which (by looking at the Frobenius x 7→ x acting on...

In this review, we consider Euclidean field theory as a formulation of quantum field theory which lives in some Euclidean space, and is expressed in probabilistic terms. Methods arising from Euclidean field theory have been introduced in a very successful way in the study of the concrete models of Constructive Quantum Field Theory. Euclidean field theory was initiated by Schwinger [1] and Nakan...

We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarki...

Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to DonaldsonUhlenbeck-Yau instantons on C, viewed as intersecting membranes of D = 7 supersymmetric Yang-Mills (SYM) theory, yields (for finite boost) a new set of 1/4 BPS equations for D = 6 SYM-Higgs...

In this talk we review recent developments which enable us to use techniques of integrable twodimensional quantum field theories to solve exactly four dimensional N=4 gauge theory through the use of the AdS/CFT correspondence. By ‘solve’ we mean here to find all anomalous dimensions of all operators of the theory for any value of the gauge coupling. We illustrate the methods with the case of th...

Part I. Classical Mechanics 9 0. Intro 9 0.1. Mechanical systems 9 0.2. Lagrangian and Hamiltonian formulation 9 1. Lagrangian approach 10 1.1. Manifolds 10 1.2. Differentiation 11 1.3. Calculus of Variations on an interval 11 1.4. Lagrangian reformulation of Newton‘s equation 13 2. Hamiltonian approach 14 2.1. Metrics: linear algebra 14 2.2. The passage to the cotangent vector bundle via the k...