124 Result(s)

Article

Complexity of Quantum Circuits via Sensitivity, Magic, and Coherence

Quantum circuit complexity—a measure of the minimum number of gates needed to implement a given unitary transformation—is a fundamental concept in quantum computation, with widespread applications ranging from...

Kaifeng Bu, Roy J. Garcia, Arthur Jaffe… in Communications in Mathematical Physics (2024)

Article

Duality of graph invariants

We study a new set of duality relations between weighted, combinatoric invariants of a graph G. The dualities arise from a non-linear transform \(\mathcal{B}\) ℬ , acting on the weight function p. We define $...

Kaifeng Bu, Weichen Gu, Arthur Jaffe in Science China Mathematics (2020)

Article

Planar Para Algebras, Reflection Positivity

We define a planar para algebra, which arises naturally from combining planar algebras with the idea of \({\mathbb{Z}_{N}}\) ...

Arthur Jaffe, Zhengwei Liu in Communications in Mathematical Physics (2017)

Article

Characterization of Reflection Positivity: Majoranas and Spins

We study linear functionals on a Clifford algebra (algebra of Majoranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient ...

Arthur Jaffe, Bas Janssens in Communications in Mathematical Physics (2016)

Article

Stochastic Quantization, Reflection Positivity, and Quantum Fields

We investigate stochastic quantization as a mathematical tool for quantum field theory. We test the method for the free scalar field. We find that the usual method of stochastic quantization is incompatible wi...

Arthur Jaffe in Journal of Statistical Physics (2015)

Article

Reflection Positivity for Parafermions

We establish reflection positivity for Gibbs trace states for a class of gauge-invariant, reflection-invariant Hamiltonians describing parafermion interactions on a lattice. We relate these results to recent w...

Arthur Jaffe, Fabio L. Pedrocchi in Communications in Mathematical Physics (2015)

Article

Complex Classical Fields: A Framework for Reflection Positivity

We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables ...

Arthur Jaffe, Christian D. Jäkel… in Communications in Mathematical Physics (2014)

Article

Quantum Field Theory on Curved Backgrounds. I. The Euclidean Functional Integral

We give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder Schrader quantization, as these methods have proved useful to establish...

Arthur Jaffe, Gordon Ritter in Communications in Mathematical Physics (2007)

Article

An Exchange Identity for Non-linear Fields

We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.

Arthur Jaffe, Christian Jäkel in Communications in Mathematical Physics (2006)

Article

The Elliptic Genus and Hidden Symmetry

We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also parti...

Arthur Jaffe in Communications in Mathematical Physics (2001)

Article

Quantum Invariants

In earlier work, we derived an expression for a partition function ?^(λ), and gave a set of analytic hypotheses under which ?^(λ) does not depend on a parameter λ. The proof that ?^(λ) is invariant involved entire c...

Arthur Jaffe in Communications in Mathematical Physics (2000)

Article

PROOF AND THE EVOLUTION OF MATHEMATICS

Arthur Jaffe in Synthese (1997)