By Nirmala Prakash
Providing the fundamentals of arithmetic which are wanted for studying the physics of this day, this publication describes in short the theories of teams and operators, finite- and infinite-dimensional algebras, ideas of symmetry and supersymmetry. It then delineates their relatives to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a bankruptcy on (the advanced thought of) strings and superstrings and their hyperlink to black holes - an idea that fascinates either the physicist and the mathematician.
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Additional info for Mathematical Perspectives on Theoretical Physics: A Journey from Black Holes to Superstrings
Sample text
What is information? In the absence of any "rigorous" definition, let us for the moment settle for the meaning attached to this word by the layman, and try to find out criteria which discriminate statements bringing forth a lot of information from statements poor in information. Compare, for instance, the two statements or messages: M1 = Professor X entered the classroom. M2 = Professor X, upon entering the classroom, shot a student. Everybody agrees that M1 is trivial and its taking place moves nobody (except perhaps the waiting students), while M2 causes an international stir (it is broadcast, televised, discussed in the press, and so on); therefore M2 brings a lot of information -especially if Professor X is well known.
Let a be an undetermined Langrangian multiplier. We consider the maximization of 47 Il F (P. 13) hence lo92Pi =a -1 for all i. Therefore all Pi are equal. From the normalization condition, we get P. =1/1l. , simply the logarithm of the number of states. Let us pass next to the physicaZ entropy of a system. Suppose we have a system (a physical body, say) composed of N interacting components which belong to Il discrete different categories according to a given classification criterion (say a discrete velocity distribution).
Acted upon, by an external observer, depending on the "filter" he is using, at three basic, distinct hierarchical levels: (1) the level of elementary particle interaction (a base level common to all physical systems), (2) the atomic level, and (3) the molecular level. Now we know that the type of interaction characterizing level 1 is the strong nuclear interaction F1 , characterizing level 2 are the electromagnetic interactions F2 , and characterizing level 3 are the London-van der Waals interactions.