add qft-propagator-poles.typ, harmonic-oscillator-energy-vs-frequency…

….typ, harmonic-oscillator-energy-vs-inv-temperature.TYP

rename vae to variational-autoencoder
rename poles to qft-propagator-poles

rename harm-osc-energy-freq to harmonic-oscillator-energy-vs-frequency
rename harm-osc-energy-inv-temp to harmonic-oscillator-energy-vs-inv-temperature

assets/harmonic-oscillator-energy-vs-freq/harmonic-oscillator-energy-vs-freq.typ

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+#import "@preview/cetz:0.3.1": canvas, draw
+#import "@preview/cetz-plot:0.1.0": plot
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#let size = (8, 5)
+
+#canvas({
+  draw.set-style(
+    axes: (
+      y: (label: (anchor: "north-west", offset: -0.2), mark: (end: "stealth", fill: black)),
+      x: (label: (anchor: "north", offset: 0.1), mark: (end: "stealth", fill: black)),
+    ),
+  )
+
+  plot.plot(
+    size: size,
+    x-min: 0,
+    x-max: 11,
+    y-min: 0,
+    x-label: $omega = sqrt(k/m)$,
+    y-label: $angle.l E angle.r \/ k_"B" T$,
+    x-tick-step: 2,
+    y-tick-step: 2,
+    axis-style: "left",
+    {
+      // Define constants from original
+      let h = 1
+      let b = 1
+
+      // Add the energy expectation value curve
+      plot.add(
+        style: (stroke: blue + 1.5pt),
+        domain: (0.01, 11), // Avoid x=0 due to division
+        samples: 200, // More samples for smoother curve
+        x => {
+          // E = (1/2)hω(1 + 4/(exp(βhω) - 1))
+          let hw = h * x
+          let exp_term = calc.exp(b * hw)
+          (1 / 2) * hw * (1 + 4 / (exp_term - 1))
+        },
+      )
+    },
+  )
+})

assets/harmonic-oscillator-energy-vs-inv-temp/harmonic-oscillator-energy-vs-inv-temp.typ

@@ -0,0 +1,45 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+#import "@preview/cetz-plot:0.1.0": plot
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#let size = (8, 5)
+
+#canvas({
+  draw.set-style(
+    axes: (
+      y: (label: (anchor: "north-west", offset: -0.2), mark: (end: "stealth", fill: black)),
+      x: (label: (anchor: "north", offset: 0.1), mark: (end: "stealth", fill: black)),
+    ),
+  )
+
+  plot.plot(
+    size: size,
+    x-min: 0,
+    x-max: 11,
+    y-min: 0,
+    y-max: 2.3,
+    x-label: $beta$,
+    y-label: $angle.l E angle.r \/ planck.reduce omega$,
+    x-tick-step: 2,
+    y-tick-step: 0.5,
+    axis-style: "left",
+    {
+      // Define constants from original
+      let (h, w) = (1, 1)
+
+      // Add the energy expectation value curve
+      plot.add(
+        style: (stroke: blue + 1.5pt),
+        domain: (1e-5, 11),
+        samples: 200, // More samples for smoother curve
+        x => {
+          // E = (1/2)hω(1 + 4/(exp(xhω) - 1))
+          let hw = h * w
+          let exp_term = calc.exp(x * hw)
+          (1 / 2) * hw * (1 + 4 / (exp_term - 1))
+        },
+      )
+    },
+  )
+})

assets/qft-propagator-poles/qft-propagator-poles.typ

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+#import "@preview/cetz:0.3.1": canvas, draw, decorations
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  import draw: line, content, circle
+
+  let xrange = 6
+  let yrange = 4
+
+  // Axes styles
+  let arrow-style = (mark: (end: "stealth", fill: black))
+  let line-style = (stroke: black + .75pt)
+  let zigzag-style = (amplitude: 0.1, segment-length: 0.2)
+
+  // Main axes
+  line((-1, 0), (2, 0), ..line-style, name: "x-axis-left")
+  decorations.zigzag(
+    line((2, 0), (xrange, 0)),
+    ..zigzag-style,
+    ..line-style,
+    name: "x-axis-right",
+  )
+  content((rel: (-0.3, 0.3), to: "x-axis-right.end"), $"Re"(p_0)$, name: "x-label")
+
+  decorations.zigzag(
+    line((2, -3), (xrange, -3), name: "lower-zigzag"),
+    ..zigzag-style,
+    ..line-style,
+  )
+
+  line((0, -yrange - 1), (0, 2), ..arrow-style, ..line-style, name: "y-axis")
+  content((rel: (0.8, -0.2), to: "y-axis.end"), $"Im"(p_0)$, name: "y-label")
+
+  // Brace for q_0
+  content(
+    (2, -1.5),
+    [#math.underbrace(box(width: 7.5em))],
+    name: "q0-brace",
+    angle: -90deg,
+  )
+  content((rel: (-0.5, 0), to: "q0-brace"), $q_0$, name: "q0-label")
+
+  // Matsubara frequencies
+  for n in range(-yrange, 2) {
+    if n != 0 {
+      circle((0, n), radius: 0.04, fill: black, name: "matsubara-" + str(n))
+      content("matsubara-" + str(n), $i omega_#n$, anchor: "west", padding: 0.2)
+    }
+  }
+  circle((0, 0), radius: 0.03, fill: black, name: "origin")
+  content((0.2, 0.1), $0$, name: "origin-label")
+
+  // Poles
+  let pole(x, y, label) = {
+    circle((x, y), radius: 0.06, fill: black, name: "pole-" + str(x) + "-" + str(y))
+    content("pole-" + str(x) + "-" + str(y), label, anchor: "south", padding: 0.1)
+  }
+
+  // First row of poles
+  pole(3, 1, $alpha_2^1$)
+  pole(5, 1, $alpha_1^1$)
+
+  // Second row
+  pole(3, -1, $alpha_2^1$)
+  pole(5, -1, $alpha_1^1$)
+
+  // Third row
+  pole(3, -2, $alpha_2^2$)
+  pole(5, -2, $alpha_1^2$)
+
+  // Fourth row
+  pole(3, -4, $alpha_2^2$)
+  pole(5, -4, $alpha_1^2$)
+
+  // Region labels
+  let blue = rgb("#00008B") // DarkBlue equivalent
+  content((4, 1.5), text(fill: blue)[(I)], name: "region-1")
+  content((4, -1.5), text(fill: blue)[(II)], name: "region-2")
+  content((4, -4.5), text(fill: blue)[(III)], name: "region-3")
+})