MASSA INVARIANTE

LORENTZ BOOST SPEED :

MOMENTUM P

$ E' = \gamma\,(E-\beta\,p)$

$ E'=\gamma\,(E-\beta\,p) \

$ \begin{pmatrix}
E'\
p'  \
\end{pmatrix}=
\begin{pmatrix}
\gamma & -\gamma \beta  \
-\gamma \beta & \gamma  \
\end{pmatrix}
\begin{pmatrix}
E\
p \
\end{pmatrix}.
 $

$ \beta $

$ E'(\beta) $

E (GeV) =

M (GeV/c2) =

Linea Rossa -> Energia nel nuovo SR :  E'

c=1   /   Energie (E) espresse in GeV

momentum P

E

M

P

A = (20.22, -9.02)
E = 8.1 (slider from 0 to 10, step 0.1)
B = Point(Circle[A, E / sqrt(2)])
a = Segment(A, B)
c = Circle(A, B)
B' = Mirror(B, A)
b = LineBisector(B', B)
C = Intersect(c, b, 2)
D = Intersect(c, b, 1)
d = Segment(C, B')
e = Segment(D, B')
f = Segment(B, D)
g = Segment(B, C)
E_1 = Intersect(d, g)
F = Intersect(d, g)
M = 3.2337 (slider from 5.0E-4 to 10, step 1.0E-4)
h = Circle(F, M)
G = Intersect(h, g, 1)
i = OrthogonalLine(G, g)
H = Intersect(h, d, 1)
j = OrthogonalLine(H, d)
I = Intersect(i, j)
k = Segment(G, I)
l = Segment(I, H)
v = 0 (slider from 0 to 1, step 0.01)
inputBox1 = Textfield(v)
γ: (1 - v^(2))^(-0.5)
J = Point(d)
p: sqrt(E^(2) - M^(2))
A3 = 0.7599342076785331
o: γ * (E - v * sqrt(E^(2) - M^(2)))
s(x) = (1 - x^(2))^(-0.5) * (E - x * sqrt(E^(2) - M^(2)))
P_1: (v, (1 - v^(2))^(-0.5) * (E - v * sqrt(E^(2) - M^(2))))
poly1, i_1, g_1, e_1, h_1 = Polygon(I, G, E_1, H)
O = Intersect(g_1, i_1)
Q = Intersect(e_1, g_1)
poly2, q_1, b_1, d_1, b' = Polygon(Q, B, D, B')
inputBox2 = Textfield(E)
inputBox3 = Textfield(M)
R = (15.359705910636118, -3.381269267379562)
S = (20.5613113030075, -3.398961802727764)
T = Midpoint(B', C)
c_1 = Circle(T, C)
f_1 = Circle(C, H)
U = Intersect(c_1, f_1, 1)
a_1 = Segment(C, U)
P = Segment(U, B')
V = Intersect(c_1, e_1, 1)
k_1 = CircleArc(V, U, H)
p_1 = CircleArc(T, V, B')
u = Distance(P, b')
r: (1 - v^(2))^(-0.5) * (E - v * sqrt(E^(2) - M^(2)))
q = Circle(C, r)
K = Intersect(q, q_1, 1)
L = Point(q)
m = OrthogonalLine(K, q_1)
n = OrthogonalLine(L, m)
N = Intersect(m, n)
W = (18.680630734886673, -3.5512681921493208)
n_1 = Segment(W, C)
r_1 = Segment(W, G)
Z = (20.381156526253346, -1.4407942189352925)
A_1 = Intersect(p_1, a_1, 1)
s_1 = Segment(Z, A_1)
t_1 = Segment(Z, B)
B_1 = (10.459075858289438, -11.699417510259103)
a_2 = Segment(U, B_1)
b_2 = Segment(B_1, B')
C_1 = Intersect(e_1, a_1)
l_1 = Segment(Z, C_1)
D_1 = Intersect(q, q_1, 1)
F_1 = Point(q)
G_1 = Intersect(d_1, P)
m_1 = Segment(C_1, G_1)
c_2 = OrthogonalLine(F_1, m_1)
d_2 = OrthogonalLine(D_1, q_1)
H_1 = Intersect(c_2, d_2)
e_2 = Segment(F_1, H_1)
f_2 = Segment(D_1, H_1)
j_1 = Segment(B_1, U)
I_1 = Point(g_1)
J_1 = Intersect(P, b_2)
g_2 = CircumcircleArc(I_1, U, J_1)
K_1 = Intersect(g_2, d_1, 1)
poly3, k_2, u_1, h_2, i_2, L_1, M_1 = Polygon(K_1, U, 4)