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  2. cosmo

    www.damtp.cam.ac.uk/user/tong/cosmo/two.pdf
    26 Jun 2024: the combined system will eventually settle down to a new equilibrium state at some. ... of the chemical potential. Now we can use the chemical potential for something new.
  3. standardmodel

    www.damtp.cam.ac.uk/user/tong/sm/standardmodel2.pdf
    26 Jun 2024: 2.1 Discrete Symmetries. The idea of spontaneous symmetry breaking is not something new: it appears in some.
  4. 31 May 2024: generate. a new solution. • Reparameterisation invariance: We introduced σ as an arbitrary parameterisationof the path. ... Then we could equally as well construct an action S̃ using this new parameter,.
  5. dynrel

    www.damtp.cam.ac.uk/user/tong/relativity/four.pdf
    3 Jul 2024: 0. It looks as if we’ve found a new conserved quantity since we’ve learnt that. ... Now that we understand orbits, let’s see how Kepler’s laws can be derived from New-.
  6. List of publications H.K. Moffatt May 24, 2024 Curriculum ...

    www.damtp.cam.ac.uk/user/hkm2/HKM_publications.pdf
    18 Jun 2024: Moffatt, H. K. 2006a Corner flow: a classical problem with a new twist. ... K. 1993d Spiral structures in turbulent flow. In New Approaches and Concepts inTurbulence (ed.
  7. PUBLICATION LIST -- J

    www.damtp.cam.ac.uk/user/tsm/jrw_publist1.pdf
    3 Jun 2024: Miklowitz and J. D. Achenbach, pp. 347-371, John Wiley, New York (l978). ... Nemat-Nasser, pp. 59-66, Pergamon, New York (1980). 51. D. R. S.
  8. cosmo

    www.damtp.cam.ac.uk/user/tong/cosmo/one.pdf
    26 Jun 2024: Preprint typeset in JHEP style - HYPER VERSION Michaelmas Term, 2019. CosmologyUniversity of Cambridge Part II Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,.
  9. Preprint typeset in JHEP style - PAPER VERSION June ...

    www.damtp.cam.ac.uk/user/tong/tasi/tasi.pdf
    31 May 2024: both physicists and mathematicians alike. They have lead to new insights into a wide. ... It. must be possible to express these three new zero modes as a linear combination of the.
  10. Preprint typeset in JHEP style - HYPER VERSION Lent ...

    www.damtp.cam.ac.uk/user/tong/relativity/dynrel.pdf
    3 Jul 2024: properties, from which we will see new concepts emerging such as energy and conserva-. ... such as the trajectory of a particle, become ill-defined. The new framework that.
  11. 2 Surfaces (and Volumes) The main purpose of this ...

    www.damtp.cam.ac.uk/user/tong/vc/vc2.pdf
    12 Jun 2024: Our new notation does, however, retain the idea of ordering. You should work from. ... with something new and exciting: an unorientable surface, known as a Möbius strip.
  12. munich_talk_mjc

    www.damtp.cam.ac.uk/user/mjc249/talks/rigged_DMD_munich.pdf
    10 Jun 2024: 20. 21. New Papers on“Koopman Operators”. number of papers. doubles every 5 yrs. ... 17. 20. 18. 20. 19. 20. 20. 20. 21. New Papers on“Koopman Operators”.
  13. 6 Tensors A famously annoying definition of a tensor ...

    www.damtp.cam.ac.uk/user/tong/vc/vc6.pdf
    12 Jun 2024: hand. I will introduce a new symbol for “dierentiation and anti-symmetrisation” and. ... connection. Here our new anti-symmetric derivative obeys D2(anything) = 0. But we.
  14. 12 Jun 2024: For. such curves, we introduce new notation and write the line integral asI. ... should be viewed as infinitesimally close to each other. These two new segments have.
  15. 12 Jun 2024: meet. The sign means that it’s good news for one, less good for the other. ... Both new terms come with. minus signs, which is appropriate because fighting is bad.
  16. BMC_talk_mjc

    www.damtp.cam.ac.uk/user/mjc249/talks/rigged_DMD_manchester.pdf
    18 Jun 2024: 20. 21. New Papers on“Koopman Operators”. number of papers. doubles every 5 yrs.
  17. 6. Large N Non-Abelian gauge theories are hard. We ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/6n.pdf
    26 Jun 2024: these properties. With these new couplings, the Yang-Mills action is. SYM = N. ... gauge theory. At this point, it is useful to introduce some new notation.
  18. 31 May 2024: However, we can build a new vector field by taking the commutator [X, Y ], which. ... We will. work with these operations frequently enough to justify introducing some new notation.
  19. 3 The Formalism of Quantum Mechanics In the previous ...

    www.damtp.cam.ac.uk/user/tong/qm/qm3.pdf
    26 Jun 2024: and gives you back a new function. Throughout these lectures we will dress any such.
  20. 5. When Gravity is Weak The elegance of the ...

    www.damtp.cam.ac.uk/user/tong/gr/five.pdf
    31 May 2024: Then do a gauge transformation (5.10). Your new gauge potential will satisfy. @ ... µhµ 12@h+ = f. So if you pick a gauge transformation µ that obeys µ = fµthen your new metric will be in de Donder gauge.
  21. 6. Black Holes Black holes are among the most ...

    www.damtp.cam.ac.uk/user/tong/gr/six.pdf
    31 May 2024: our old coordinates, we’re instead going to find a new set of coordinates that works. ... everywhere. Our first step is to introduce a new radial coordinate, r?, defined by.
  22. 4 A Quantum Particle in Three Dimensions We will ...

    www.damtp.cam.ac.uk/user/tong/qm/qm4.pdf
    26 Jun 2024: imuthal angular momentum). Before we get going, let’s introduce some new variables. ... plifying things, we’ve introduced a new physical constant c, the speed of light.
  23. Koopman_turing_talk_mjc

    www.damtp.cam.ac.uk/user/mjc249/talks/rigged_DMD_turing.pdf
    23 May 2024: 20. 21. New Papers on“Koopman Operators”. number of papers. doubles every 5 yrs. ... 17. 20. 18. 20. 19. 20. 20. 20. 21. New Papers on“Koopman Operators”.
  24. topicsinqm

    www.damtp.cam.ac.uk/user/tong/aqm/topics1.pdf
    2 Jul 2024: E, so the new Hamiltonian reads. H = 2. 2mr2 V (r) ex E.
  25. topicsinqm

    www.damtp.cam.ac.uk/user/tong/aqm/topics4.pdf
    2 Jul 2024: 4. Atoms in Electromagnetic Fields. Our goal in this chapter is to understand how atoms interact with electromagnetic. fields. There will be several stages to our understanding. We start by looking at atoms. in constant, background electromagnetic
  26. standardmodel

    www.damtp.cam.ac.uk/user/tong/sm/standardmodel4.pdf
    26 Jun 2024: 165 –. symmetry U(1)0Vand a new axial symmetry U(1)0. A, under which the quarks transform. ... So in this case,. the surviving discrete symmetry doesn’t tell us anything new.
  27. 4. Lattice Gauge Theory Quantum field theory is hard. ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/4lattice.pdf
    26 Jun 2024: This then leaves us with a new theory defined on a lattice with spacing 2a. ... and 4 are left-handed. We see that, once again, the lattice has generated new gapless.
  28. standardmodel

    www.damtp.cam.ac.uk/user/tong/sm/standardmodel1.pdf
    26 Jun 2024: If you’re completely new to the wonderful world of subatomic particles, this is a good. ... in Section 1.4. For massive particles, this doesn’t buy us anything new: the set of.
  29. 5. Chiral Symmetry Breaking In this section, we discuss ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/5chisb.pdf
    26 Jun 2024: solution U?(x) with energy E? Then the new configuration U(x) = U?(x) has energy. ... can be used to generate new solutions. These are trivially related to the original,.
  30. dynrel

    www.damtp.cam.ac.uk/user/tong/relativity/five.pdf
    3 Jul 2024: We can write this by introducing a new vector! = ̇ẑ,.
  31. topicsinqm

    www.damtp.cam.ac.uk/user/tong/aqm/topics5.pdf
    2 Jul 2024: We’ll introduce. some new notation for this state that will become useful in the following section: we.
  32. 4. The Einstein Equations It is now time to ...

    www.damtp.cam.ac.uk/user/tong/gr/four.pdf
    31 May 2024: M, we can usethis to map all fields, including the metric, on M to a new set of fields on M.
  33. dynrel

    www.damtp.cam.ac.uk/user/tong/relativity/seven.pdf
    3 Jul 2024: transformations are a property of space and time themselves. With Einstein’s new take on the principle of relativity, all problems with Maxwell’s. ... there was a new, fundamental constant of Nature – let’s call it – given by.
  34. 3. Introducing Riemannian Geometry We have yet to meet ...

    www.damtp.cam.ac.uk/user/tong/gr/three.pdf
    31 May 2024: Z). = fR(!; X, Y, Z). Thus, both torsion and curvature define new tensors on our manifold. – ... change of coordinates to xµ(x̃) which does the trick. In the new coordinates,.
  35. Koop_italy_mjc

    www.damtp.cam.ac.uk/user/mjc249/talks/Koopman_workshop_mjc.pdf
    20 May 2024: New program on foundations and classification for Koopman. 50. Summary: Infinities matter. •
  36. Preprint typeset in JHEP style - HYPER VERSION 2018 ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/1em.pdf
    26 Jun 2024: mathematical construct known as a fibre bundle. This brings something new to the. ... The equations (1.13) carry much – although not all – of the new physics.
  37. standardmodel

    www.damtp.cam.ac.uk/user/tong/sm/standardmodel3.pdf
    26 Jun 2024: magnetic or paramagnetic. Except now there is a new ingredient which does not show.
  38. 2. Yang-Mills Theory Pure electromagnetism is a free theory ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/2ym.pdf
    26 Jun 2024: This new way of looking at things starts with a question: why should we insist that the. ... general wavefunctions doesn’t give any new physics. Instead, it allows for a dierent.
  39. J. Fluid Mech. (2024), vol. 988, A11, doi:10.1017/jfm.2024.260 Fast…

    www.damtp.cam.ac.uk/user/hinch/publications/JFM988_A11.pdf
    31 May 2024: J. Fluid Mech. (2024), vol. 988, A11, doi:10.1017/jfm.2024.260. Fast flow of an Oldroyd-B model fluid through anarrow slowly varying contraction. John Hinch1,†, Evgeniy Boyko2 and Howard A. Stone3. 1DAMTP-CMS, Cambridge University, Wilberforce Road
  40. 27 Apr 2024: Lent Term, 2015. ElectromagnetismUniversity of Cambridge Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,. Wilberforce Road,. Cambridge, CB3 OBA, UK.
  41. J. Fluid Mech. (2024), vol. 988, A10, doi:10.1017/jfm.2024.223 Flow…

    www.damtp.cam.ac.uk/user/hinch/publications/JFM988_A10.pdf
    10 Jun 2024: J. Fluid Mech. (2024), vol. 988, A10, doi:10.1017/jfm.2024.223. Flow of an Oldroyd-B fluid in a slowly varyingcontraction: theoretical results for arbitraryvalues of Deborah number in the ultra-dilutelimit. Evgeniy Boyko1,†, John Hinch2 and Howard
  42. topicsinqm

    www.damtp.cam.ac.uk/user/tong/aqm/topics3.pdf
    2 Jul 2024: 3.5). and our new goal is to compute the expectation values h1/rin,l and h1/r2in,l for thehydrogen atom wavefunctions. ... This time, we introducea new “radial momentum” observable. p̃ = i@.
  43. dynrel

    www.damtp.cam.ac.uk/user/tong/relativity/two.pdf
    3 Jul 2024: properties, from which we will see new concepts emerging such as energy and conserva-. ... such as the trajectory of a particle, become ill-defined. The new framework that.

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