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The Theoretical Physics MSc is an intensive, research-led course in which you will examine basic topics in theoretical and mathematical physics such as general relativity and quantum field theory, before exploring advanced topics such as string theory, supersymmetry and integrable quantum field theory. Our highly rated research programme will equip you with the knowledge The Theoretical Physics MSc is an intensive, research-led course in which you will examine basic topics in theoretical and mathematical physics such as general relativity and quantum field theory, before List of Universities Offering a course in M.

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Only the Doctor of Philosophy Ph. The Utrecht Summer School in Theoretical Physics offers a blend of advanced undergraduate material in thermal and statistical physics, quantum mechanics and electrodynamics. Prospective Physics Graduate Students. Theses degrees also focus on both theoretical and practical aspects of the fields. The Master stage takes typically one and a half years, the last half year of which is devoted to the master thesis. I was also a mechanical engineering undergrad at Delhi Technological University and gave my JAM exam in my final year. Physics , two year M.

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Andhra University. But to be a theoretical physicist today, you pretty much have to stake your career on one incredibly popular but pretty much unprovable notion: string theory. Ever since its establishment, the Department has played a key role in strengthening postgraduate teaching and research in physics through active contact and collaboration with several research institutes and universities in India and abroad as The Department of Physics is known internationally for its top-class research. This is a comprehensive and precise coverage of the mathematical concepts and tools used in present theoretical physics: differential geometry, Lie groups, fiber bundles, Clifford algebra, differential operators, normed algebras, connections, etc.

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Through this project, students develop their skills in teamwork, communication, presentation and IT skills. The Centre's activities are mainly in the areas of astrophysics, gravitation, cosmology and high energy physics. Admissions closed The following is a list of candidates who have been provisionally selected for admission to the MSc Physics programme subject to their appearing at a counselling session to be conducted at the Belur main campus on 18 June Tuesday at 12 noon. This function plays an important role to estimate the number of zeros of Rimann zeta function in the critical strip up to a height t.

The MSc programmes in Theoretical Physics and Mathematical Physics introduce advanced ideas in theoretical physics and apply them to solving real-world problems. Tata Institute of Fundamental Research is a National Centre of the Government of India, under the umbrella of the Department of Atomic Energy, as well as a deemed University awarding degrees for master's and doctoral programs. Let S t be the argument of the Riemann zeta function on the critical line. You might need to get a B.

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We also make some remarks on the problem of UV completeness of such integrable deformations. The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way.

The first of these scalars, Xi, coincides with the composite field TT built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by Xi are "solvable" in a certain sense, even if the original theory is not integrable.

The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. Published by Elsevier B. Given an IQFT, we will try to enumerate all its infinitesimal deformations which preserve integrability. We mostly ignore the profound question of ultraviolet UV completeness, assuming that the theory has UV cutoff. The scalars Xs can be defined in terms of the components of the local currents associated with the corresponding IM Sect.

Alternatively, in massive theories, the fields Xs are identified with special solutions of the form factor bootstrap equations, relating them to the deformations of the factorizable S-matrix via the CDD factor Sect. We illustrate the situation by explicit construction in the case of the sine-Gordon model Sect.

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The field Xi is identical to the composite field TT. We show that the deformations generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable, and we discuss some properties of such deformations Sect. Our calculations in Sects. Our statements below apply to QFT understood as "effective field theories", in which all UV pathologies can be hidden under a short-distance cutoff.

However, in Sect. Here z e. Then the points z can be labeled by complex coordinates, which are denoted z, z,. The correlation functions 2. One might or might not think in terms of Lagrangian QFT, where the theory is described by some sort of local action. As was mentioned, in this discussion we mostly ignore the problem of UV completeness of the theory, assuming that some UV regularization with the microscopic cutoff distance e is imposed. The density L may involve higher derivatives of the fundamental fields, i. Let again Fg be the space of local fields in Ag. Generic variation of the action 2.

The Lagrangian approach formulation makes self evident the following deformation formula. In what follows we will not explicitly refer to any Lagrangian representation, but simply postulate the above deformation formula. Then the bi-local products as in the l. Although this assumption is not crucial for our conclusions below, it considerably shortens some of our arguments. One of the common characteristics of Integrable Field Theories is the presence of an infinite set of commutative local Integrals of Motion IM.

Local IM are generated by local currents, i. Below we also use conventional notations. In what follows it will be convenient to use separate notations for negative s, i. The negative-s equations 3. The notion of integrability requires that the operators4 Ps form a commutative set,.

When there are more than one current of the same spin, additional labels may be introduced. Supersymmetry provides an interesting extension, but we do not discuss it here. Let us remind here that the commutators [Ps, O z ] with any local field O can be defined, in the Euclidean language, by the integrals. Let us note here that generally the dimensions are defined relative to a given fixed point; Generally, if QFT has a more complicated UV structure, the notion of dimensions may be ambiguous. Of course generally such limits are singular, demanding subtractions and thus making the result ambiguous.

It turns out that if one takes OPE in the special combination. Let us note that the "derivative terms" may well involve divergent coefficients, therefore this definition of Xs is unambiguous only up to the derivatives. Fortunately we are interested in the fields as the vectors in FF, so the derivatives are irrelevant. Let us show that the limit in 4.

The following calculations are nearly identical to those presented in Ref. Consider, say, the Z derivative of the combination 4. As the consequence of the continuity equations 3. Now, plug in the OPE of the products appearing in the r. Since all the coefficient functions depend on the separation z - z! Similar calculation reveals that the dz derivative of 4. That is, both 9z and dz of the operator product 4. In turn, it follows that the OPE of 4. The value of the coefficient is irrelevant, since it can be absorbed in the normalization of the field Xs below.

Setting this coefficient to one for every s brings the OPE of 4. Some useful properties of these operators are worth noting. Consider IQFT in the geometry of an infinite cylinder, with the spatial coordinate x compactified on a circle with some finite circumference R. Then, by repeating the arguments in [2], one can prove that. This simply means that adding such fields as the perturbations to the action as we do in Sect.

We make further remarks on this point in Sect. The operator X1 is special. It is built from the components 3. It is identical to the field TT , a frequent actor in a number of previous studies []. A general definition can be found in [2]. Here we use the notations X1 and TT interchangeably.


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  • Infinitesimal deformations generated by this operator turn out to be in some sense "solvable", even if the original theory is not integrable. Then, as was shown in [2], the equation 4. Since, by definition of A, an infinitesimal shift of a is generated by TT a, this leads to closed differential equation for the energy levels,. The equation has the same form for all eigenvalues En R, a ; for this reason we dropped the index n. Since in what follows a is generally regarded as the parameter, we use instead the abbreviated notation.

    Let us note here some properties of the solutions of equation 5. The above equation yields the a -dependence of the bulk vacuum energy density Fa. Furthermore, if the theory is massive, it follows from 5. Since this equation applies to any particle of the theory, the mass ratios in Aa are independent of a.

    It is not difficult to show that consistency of 5. If the theory A0 is integrable, the theories A are integrable as well see Sect. In that case the ground state energy of the finite-size system can be found using the Thermodynamic Bethe Ansatz TBA technique [8] for a review see e.

    It is not difficult to show that the deformation 5. Mathematically, shocks are algebraic square-root singularities of E R, a. This follows from an alternative form of Eq.

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    Both at positive and negative aC, the form 5. A possible connection. We will comment on this point elsewhere [10]. Here we note that the finite size spectrum 5. To this end, let us first prove that the commutator of any local IM Pa with any of the fields Xs z is a total derivative of a local field, i. Here the commutator can be understood as the contour integral 3. To prove 6. The commutator naturally splits into "z-terms", the terms generated by commuting Pa with the densities localized at z, and "z'-terms" from the commutations with the densities at z'.

    Recalling the relations 3. Similar calculation using 3. Therefore, the whole commutator 6. Consider the correlation function. Oan zn , and the z, z integration is over some closed contour C. According to the deformation formula 2.

    Multipoint Green's functions in 1+1 dimensional integrable quantum field theories - Hrachya Babujian

    To see that this is always possible, let us assume for simplicity that the contour C is simple, and focus on the first term in the r. Split the integration over w into two parts,7. Then the second term in 6. A non-zero contribution may arise from the first term, where w falls inside C.

    With w e D C fixed, one can collapse the contour C on w, thus reducing the integral over z to the commutator [Pa, Xs w ] see 3. The latter statement means that. Thus, in the remaining integral over w the integrand is written as a total derivative, and the integral reduces to the boundary contribution, i. As a result, the first term in the r. We conclude that after infinitesimal deformation generated by the operator Xs the integral Pa, Eq. Although at the moment we do not have satisfactory proof of this statement, we find its general validity very likely.

    One of the arguments is as follows. A priori, there are two possibilities. In both cases the IM of the deformed theory would form a non-Abelian algebra of local higher spin IM, which would provide extremely powerful symmetry structure, so far unknown outside CFT or free massive QFT.

    Therefore, breakdown of the commutativity under deformation is unlikely: it would be "too good to be true". The first step has been performed for a large number of models and also the second one for several models. The third step is unsolved up to now. Here the program is illustrated in terms of the sine-Gordon model alias the massive Thirring model. Exploiting the "off-shell" Bethe Ansatz we propose general formulae for form factors.


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