• E C G Sudarshan

      Articles written in Pramana – Journal of Physics

    • Interaction between classical and quantum systems and the measurement of quantum observables

      E C G Sudarshan

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      Quantum mechanics presumes classical measuring instruments with which they interact. The problem of measurement interaction between classical and quantum systems is posed and solved. The restriction to compatible measurements comes about naturally as the condition for the integrity of the classical system. A technical device is the perspective on classical mechanics as quantum mechanics with essentially hidden dynamical variables.

    • New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

      N Mukunda E C G Sudarshan

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      In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

    • Embedding of non-simple Lie groups, coupling constant relations and non-uniqueness of models of unification

      J Pasupathy E C G Sudarshan

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      A general derivation of the coupling constant relations which result on embedding a non-simple group like SUL (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SUL (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SUL (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin2ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE6, while addition of extra charged fermion singlets can reduce the value of sin2 ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.

    • The three faces of Maxwell’s equations

      N Mukunda E C G Sudarshan

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      In dealing with electromagnetic phenomena and in particular the phenomena of optics, despite the recognition of the quanta of light people tend to talk of the amplitudes and field strengths, as if the electromagnetic field were a classical field. For example we measure the wavelength of light by studying interference fringes. In this paper we study the interrelationship of three ways of looking at the problem: in terms of classical wave fields, wave function of the photon; and the quantized wave field. The comparison and contrasts of these three modes of description are carefully analyzed in this paper. The ways in which these different modes complement our intuition and insight are also discussed.

    • A basis-free approach to time-reversal for symmetry groups

      L C Biedenharn E C G Sudarshan

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      We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2isospin,SU3flavor,SU3nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.

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