scholarly journals Broken Symmetry and Yang–Mills Theory

2014 ◽  
Vol 03 (01) ◽  
pp. 54-67 ◽  
Author(s):  
François Englert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Yang Mills

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang–Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues.

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

THE FIRST DONALDSON INVARIANT AS THE WINDING NUMBER OF A NICOLAI MAP

1988 ◽  
Vol 03 (17) ◽  
pp. 1647-1650 ◽  
Author(s):  
P. MANSFIELD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Winding Number ◽  
Relativistic Quantum Field Theory ◽  
Yang Mills ◽  
Stochastic Map

We show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories.

scholarly journals Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

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