Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe universal C*-algebra of the electromagnetic field
112
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of this field such as Maxwells equations, Poincare covariance and Einstein causality. Moreover, topological properties of the field resulting from Maxwells equations are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.
rate research
Read More
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of spacelike linearity. Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.
A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag-Kastler axioms, with insights gained in the perturbative approach to quantum field theory. Key ingredients are an appropriate version of Bogolubovs relative $S$-operators and a reformulation of the Schwinger-Dyson equations. These are used to define for any classical relativistic Lagrangean of a scalar field a non-trivial local net of C*-algebras, encoding the resulting interactions at the quantum level. The construction works in any number of space-time dimensions. It reduces the longstanding existence problem of interacting quantum field theories in physical spacetimeto the question of whether the C*-algebras so constructed admit suitable states, such as stable ground and equilibrium states. The method is illustrated on the example of a non-interacting field and it is shown how to pass from it within the algebra to interacting theories by relying on a rigorous local version of the interaction picture.
Using the fact that the algebra M := M_N(C) of NxN complex matrices can be considered as a reduced quantum plane, and that it is a module algebra for a finite dimensional Hopf algebra quotient H of U_q(sl(2)) when q is a root of unity, we reduce this algebra M of matrices (assuming N odd) into indecomposable modules for H. We also show how the same finite dimensional quantum group acts on the space of generalized differential forms defined as the reduced Wess Zumino complex associated with the algebra M.
In this work we discuss the elements required for the construction of the operator algebra for the space of paths over a simply laced $SU(3)$ graph. These operators are an important step in the construction of the bialgebra required to find the partition functions of some modular invariant CFTs. We define the cup and cap operators associated with back-and-forth sequences and add them to the creation and annihilation operators in the operator algebra as they are required for the calculation of the full space of essential paths prescribed by the fusion algebra. These operators require collapsed triangular cells that had not been found in previous works; here we provide explicit values for these cells and show their importance in order for the cell system to fulfill the Kuperberg relations for $SU(3)$ tangles. We also find that demanding that our operators satisfy the Temperley-Lieb algebra leads one naturally to consider operators that create and annihilate closed triangular sequences, which in turn provides an alternative the cup and cap operators as they allow one to replace back-and-forth sequences with closed triangular ones. We finally show that the essential paths obtained by using closed triangles are equivalent to those obtained originally using back-and-forth sequences.
We present Painlev{e} VI sigma form equations for the general Ising low and high temperature two-point correlation functions $ C(M,N)$ with $M leq N $ in the special case $ u = -k$ where $ u = , sinh 2E_h/k_BT/sinh 2E_v/k_BT$. More specifically four different non-linear ODEs depending explicitly on the two integers $M $ and $N$ emerge: these four non-linear ODEs correspond to distinguish respectively low and high temperature, together with $ M+N$ even or odd. These four different non-linear ODEs are also valid for $M ge N$ when $ u = -1/k$. For the low-temperature row correlation functions $ C(0,N)$ with $ N$ odd, we exhibit again for this selected $ u = , -k$ condition, a remarkable phenomenon of a Painleve VI sigma function being the sum of four Painleve VI sigma functions having the same Okamoto parameters. We show in this $ u = , -k$ case for $ T < T_c $ and also $ T > T_c$, that $ C(M,N)$ with $ M leq N $ is given as an $ N times N$ Toeplitz determinant.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
