# Adding extra coordinate axis to plot

I am trying to make a plot just like the top one on page 9 in this paper. I don't know how to add an extra set of coordinate axis, and tilt them accordingly. I would also like to be able to label the axis.

Here is my code so far:

F1 := Plot[(-x^2)/2 + (x^4)/4, {x, -5, 5}, PlotRange -> {-1, 1}, PlotStyle -> {Black}]

F2 := Graphics[{Black, Thick, Dashed, Circle[{0, -0.25}, {1.0, 0.12}]}]

Show[F1, F2, AspectRatio -> 1/2, ImageSize -> Full, Axes -> {False, False}]


So I want a new set of coordinate axis with origin (x,y)=(1,-0,25). I don't know if my code so far is the optimal way of doing what i am trying, but it works, and i understand why and how it works. I am very new to Mathematica so bear with me if this is an easy question. I have searched without luck for answers before asking this question.

Plot[-(x^2/2) + x^4/4, {x, -3, 3}, PlotRange -> {-0.5, 1},
PlotStyle -> {Black}, AxesStyle -> Arrowheads[{0.0, 0.03}],
Ticks -> None,
Arrow[{{0.8, -0.25}, {1.5, -0.25}}],
Arrow[{{0.9, -0.35}, {1.2, -0.15}}], Dashed,
Circle[{0, -0.25}, {1., 0.12}], Line[{{-1, -0.25}, {-1, 0}}],
Text["-v", {-1, 0.05}],
Text["\!$$\*TagBox[SubscriptBox[\"ϕ\", \"1\"],\n \ DisplayForm]$$", {3, -0.1}],
Text["\!$$\*TagBox[SubscriptBox[\"ϕ\", \"2\"],\n \ DisplayForm]$$", {0.7, 0.3}],
Text[DisplayForm["v(Φ)"], {0.25, 0.95}],
Text["η", {1.6, -0.25}],
Text[DisplayForm["ε"], {1.1, -0.15}]}] • That was a very quick and perfect answer. Thank you very much! I am amazed by the efficiency of the mathematica stackexchange. – Yuki Dec 31 '16 at 12:56