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16 Oct 2021: 1.24). Here, the notation. {. s. i. }. |. m. (. 𝐱. ). means that we sum over all configurations of spins such that the coarse graining yields. ... We will invoke one last notational flourish. We’re left in (1.24) with a sum over all possible

18 Oct 2021: and. -. 𝑑. x. x. e. -. a. x. 2. =. 0. (2.24). where the second equality follows because the integrand is odd (and suitably well behaved at infinity). ... σ. ). exp. (. -. x. 2. σ. |. α. |. 2. ). =. k. 0. where, to get the final equality, we did the

18 Oct 2021: ρ. =. e. -. β. H. Z. (1.24). If we make a measurement described by an operator. ... In the quantum context, it is sometimes written in terms of the density matrix (1.24) as.

18 Oct 2021: ϕ. (. y. ). (1.24). A priori, there’s no reason for this.

25 Oct 2021: CHRIS/6, Version 10, 24.04.18 University of Cambridge – CV Cover Sheet Part 1, Page 1 of 4. ... CHRIS/6, Version 10, 24.04.18 University of Cambridge – CV Cover Sheet Part 1, Page 2 of 4.

18 Oct 2021: v. r. (. p. ). Figure 23: An incoming anti-fermion. Figure 24: An outgoing anti-fermion. •.

16 Oct 2021: 5 When Gravity is Weak. 5 When Gravity is Weak. The elegance of the Einstein field equations ensures that they hold a special place in the hearts of many physicists. However, any fondness you may feel for these equations will be severely tested if

25 Oct 2021: CHRIS/5, Version 10, 24.04.18 University of Cambridge – CV Cover Sheet Part 3, Page 1. ... CHRIS/5, Version 10 24.04.18 University of Cambridge – CV Cover Sheet Part 3, Page 2.

16 Oct 2021: ζ. Δ. ϕ. ϕ. (. 𝐱. ). Figure 24: RG flows when.

18 Oct 2021: 2 Classical Gases. 2 Classical Gases. Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, flying around in a box. Although much of the